ExpRep-package: Experiment Repetitions
In ExpRep: Experiment Repetitions
Description
Details
Author(s)
References
Examples
Description
The package ExpRep, which basically responds to educational purposes, allows to calculate
the probabilities of occurrences of an event in a great number of repetitions of
Bernoulli experiment, through the application of the local and the integral theorem of
De Moivre Laplace, and the theorem of Poisson. It gives the possibility to show the results
graphically and analytically, and to compare the results obtained by the application of the
above theorems with those calculated by the direct application of the Binomial formula.
Details
The DESCRIPTION file:
This package was not yet installed at build time.
Index: This package was not yet installed at build time.
Author(s)
Larisa Zamora-Matamoros and Jorge Diaz-Silvera
Maintainer: Larisa Zamora-Matamoros <larisa@uo.edu.cu>
References
Gnedenko, B. V. (1978). The Theory of Probability. Mir Publishers. Moscow.
Examples
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ProbL<-Local_Theorem(n=100,m=50,p=0.02)
ProbL
ProbI<-Integral_Theorem(n=100,p=0.5,linf=0,lsup=50)
ProbI
ProbP<-Poisson_Theorem(n=100,m=50,p=0.002)
ProbP
beta<-ApplicIntegralTheo(Applic="beta",n=369,p=0.4,alpha=0.05)
beta
alpha<-ApplicIntegralTheo(Applic="alpha",n=369,p=0.4,beta=0.95)
alpha
n<-ApplicIntegralTheo(Applic="n",p=0.4,alpha=0.05,beta=0.95)
n
S_Local_Limit_Theorem(n = 170, p = 0.5, Compare = TRUE, Table = TRUE, Graph = TRUE,
GraphE = TRUE)
S_Poisson_Theorem(n = 169, p = 0.002, Compare = TRUE, Table = TRUE, Graph = TRUE,
GraphE = TRUE)
S_Integral_Theorem(n=100, p=0.5, linf = 0, lsup = 50, Compare = TRUE, Table = TRUE,
Graph = TRUE, GraphE = TRUE)
Buffon(p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500))
Example output
[1] 1.570307e-256
[1] 0.5
[1] 3.030861e-100
[1] 0.95006827243625058
[1] 0.049985095799422834
[1] 369
m x PBinomial TLocal
1 0 -13.03840481040529653 6.6819117752305559e-52 7.4419138643607013e-39
2 1 -12.88501181263582218 1.1359250017891868e-49 5.4345583489117509e-38
3 2 -12.73161881486634783 9.5985662651187374e-48 3.8763696021741189e-37
4 3 -12.57822581709687348 5.3751971084665718e-46 2.7006444336879435e-36
5 4 -12.42483281932740091 2.2441447927847241e-44 1.8377690984236611e-35
6 5 -12.27143982155792656 7.4505607120452671e-43 1.2215065128760695e-34
7 6 -12.11804682378845222 2.0489041958124106e-41 7.9301597373135953e-34
8 7 -11.96465382601897787 4.8002898301891583e-40 5.0286266217181697e-33
9 8 -11.81126082824950352 9.7805905290106760e-39 3.1145703961477821e-32
10 9 -11.65786783048002917 1.7605062952218917e-37 1.8842052899791108e-31
11 10 -11.50447483271055660 2.8344151353071975e-36 1.1133701987435749e-30
12 11 -11.35108183494108225 4.1227856513559951e-35 6.4258749910530849e-30
13 12 -11.19768883717160790 5.4626909880467249e-34 3.6224821896093798e-29
14 13 -11.04429583940213355 6.6392705854720298e-33 1.9946263479627000e-28
15 14 -10.89090284163265920 7.4454677279936815e-32 1.0727490794078742e-27
16 15 -10.73750984386318486 7.7432864371137072e-31 5.6352872156522522e-27
17 16 -10.58411684609371051 7.5013087359536756e-30 2.8914472079863166e-26
18 17 -10.43072384832423793 6.7953032078638413e-29 1.4490914207904825e-25
19 18 -10.27733085055476359 5.7760077266841887e-28 7.0934515943270875e-25
20 19 -10.12393785278528924 4.6208061813474098e-27 3.3915696477242618e-24
21 20 -9.97054485501581489 3.4887086669172374e-26 1.5838905832131320e-23
22 21 -9.81715185724634054 2.4919347620838077e-25 7.2248846868644842e-23
23 22 -9.66375885947686619 1.6877194525022136e-24 3.2189777095440539e-22
24 23 -9.51036586170739362 1.0860107781318568e-23 1.4008328742913487e-21
25 24 -9.35697286393791927 6.6518160160576584e-23 5.9543723204776714e-21
26 25 -9.20357986616844492 3.8846605533776366e-22 2.4721052418186992e-20
27 26 -9.05018686839897057 2.1664453086144553e-21 1.0024881094659756e-19
28 27 -8.89679387062949623 1.1554374979277373e-20 3.9707524370429841e-19
29 28 -8.74340087286002188 5.9009843644165918e-20 1.5361997793645551e-18
30 29 -8.59000787509054753 2.8894475163695049e-19 5.8050222942283077e-18
31 30 -8.43661487732107496 1.3580403326936764e-18 2.1426014371814620e-17
32 31 -8.28322187955160061 6.1330853734552610e-18 7.7243189477036549e-17
33 32 -8.12982888178212626 2.6640589590946176e-17 2.7199461796138341e-16
34 33 -7.97643588401265191 1.1140610192577334e-16 9.3549555743936295e-16
35 34 -7.82304288624317756 4.4890105775973291e-16 3.1427110644852564e-15
36 35 -7.66964988847370410 1.7443012530093037e-15 1.0312132532960704e-14
37 36 -7.51625689070422975 6.5411296987848212e-15 3.3050179591336516e-14
38 37 -7.36286389293475541 2.3689496746950673e-14 1.0346190432549043e-13
39 38 -7.20947089516528195 8.2913238614324112e-14 3.1635042202076297e-13
40 39 -7.05607789739580760 2.8062942300233449e-13 9.4479519267978745e-13
41 40 -6.90268489962633325 9.1906136033265523e-13 2.7560572698411681e-12
42 41 -6.74929190185685979 2.9140969961766280e-12 7.8527199052172838e-12
43 42 -6.59589890408738544 8.9504407739712559e-12 2.1854117949406021e-11
44 43 -6.44250590631791109 2.6643172536471990e-11 5.9405651698871143e-11
45 44 -6.28911290854843674 7.6901884366636397e-11 1.5772609560369330e-10
46 45 -6.13571991077896328 2.1532527622657907e-10 4.0903516608474877e-10
47 46 -5.98232691300948893 5.8512303322440968e-10 1.0360937362164591e-09
48 47 -5.82893391524001458 1.5437288536133231e-09 2.5634140201581425e-09
49 48 -5.67554091747054112 3.9558051873841431e-09 6.1946927217086197e-09
50 49 -5.52214791970106678 9.8491476094055301e-09 1.4621842059507159e-08
51 50 -5.36875492193159243 2.3834937214761211e-08 3.3710540397483414e-08
52 51 -5.21536192416211897 5.6082205211203769e-08 7.5912037280779167e-08
53 52 -5.06196892639264462 1.2834196961794589e-07 1.6696939963261641e-07
54 53 -4.90857592862317027 2.8574249839467164e-07 3.5871078186222288e-07
55 54 -4.75518293085369681 6.1910874652178859e-07 7.5271969901508153e-07
56 55 -4.60178993308422246 1.3057566290277394e-06 1.5427780080438974e-06
57 56 -4.44839693531474811 2.6814645060391950e-06 3.0885518982983557e-06
58 57 -4.29500393754527376 5.3629290120784096e-06 6.0393148798809450e-06
59 58 -4.14161093977580030 1.0448465144221465e-05 1.1534579060157566e-05
60 59 -3.98821794200632596 1.9834374511064674e-05 2.1517763650859156e-05
61 60 -3.83482494423685205 3.6693592845468994e-05 3.9207921690589931e-05
62 61 -3.68143194646737770 6.6168773983632875e-05 6.9780136964352985e-05
63 62 -3.52803894869790380 1.1632897361638936e-04 1.2130288201060519e-04
64 63 -3.37464595092842989 1.9942109762809311e-04 2.0596419432700153e-04
65 64 -3.22125295315895555 3.3340714759697167e-04 3.4158094975963397e-04
66 65 -3.06785995538948164 5.4371011761967407e-04 5.5332062959365298e-04
67 66 -2.91446695762000729 8.6499336894037835e-04 8.7547024360817047e-04
68 67 -2.76107395985053339 1.3426762741761313e-03 1.3529670585599644e-03
69 68 -2.60768096208105948 2.0337596505902965e-03 2.0422756642438150e-03
70 69 -2.45428796431158514 3.0064273095682806e-03 3.0110835637272653e-03
71 70 -2.30089496654211123 4.3378451180913795e-03 4.3362325031843551e-03
72 71 -2.14750196877263688 6.1096410113963169e-03 6.0993508950584968e-03
73 72 -1.99410897100316298 8.4007563906699344e-03 8.3798449647355094e-03
74 73 -1.84071597323368885 1.1277727757337718e-02 1.1245263983321315e-02
75 74 -1.68732297546421495 1.4782967465699435e-02 1.4739563839334460e-02
76 75 -1.53392997769474082 1.8922198356095286e-02 1.8870391748974823e-02
77 76 -1.38053697992526669 2.3652747945119110e-02 2.3597093114758723e-02
78 77 -1.22714398215579257 2.8874783205729809e-02 2.8821554614928656e-02
79 78 -1.07375098438631844 3.4427626129908621e-02 3.4384095576540964e-02
80 79 -0.92035798661684443 4.0092931695589792e-02 4.0066288543874909e-02
81 80 -0.76696498884737041 4.5605709803733407e-02 4.5601794132324194e-02
82 81 -0.61357199107789628 5.0673010893037079e-02 5.0695107843085743e-02
83 82 -0.46017899330842221 5.4998755725369511e-02 5.5046724165688482e-02
84 83 -0.30678599553894814 5.8311933781114697e-02 5.8381898481733786e-02
85 84 -0.15339299776947407 6.0394502844725924e-02 6.0479230098047461e-02
86 85 0.00000000000000000 6.1105026407605040e-02 6.1194952327765867e-02
87 86 0.15339299776947407 6.0394502844725924e-02 6.0479230098047461e-02
88 87 0.30678599553894814 5.8311933781114697e-02 5.8381898481733786e-02
89 88 0.46017899330842221 5.4998755725369511e-02 5.5046724165688482e-02
90 89 0.61357199107789628 5.0673010893037100e-02 5.0695107843085743e-02
91 90 0.76696498884737041 4.5605709803733394e-02 4.5601794132324194e-02
92 91 0.92035798661684443 4.0092931695589806e-02 4.0066288543874909e-02
93 92 1.07375098438631844 3.4427626129908621e-02 3.4384095576540964e-02
94 93 1.22714398215579257 2.8874783205729809e-02 2.8821554614928656e-02
95 94 1.38053697992526669 2.3652747945119110e-02 2.3597093114758723e-02
96 95 1.53392997769474082 1.8922198356095279e-02 1.8870391748974823e-02
97 96 1.68732297546421495 1.4782967465699435e-02 1.4739563839334460e-02
98 97 1.84071597323368885 1.1277727757337708e-02 1.1245263983321315e-02
99 98 1.99410897100316298 8.4007563906699344e-03 8.3798449647355094e-03
100 99 2.14750196877263688 6.1096410113963169e-03 6.0993508950584968e-03
101 100 2.30089496654211123 4.3378451180913795e-03 4.3362325031843551e-03
102 101 2.45428796431158514 3.0064273095682806e-03 3.0110835637272653e-03
103 102 2.60768096208105948 2.0337596505902965e-03 2.0422756642438150e-03
104 103 2.76107395985053339 1.3426762741761300e-03 1.3529670585599644e-03
105 104 2.91446695762000729 8.6499336894037835e-04 8.7547024360817047e-04
106 105 3.06785995538948164 5.4371011761967407e-04 5.5332062959365298e-04
107 106 3.22125295315895555 3.3340714759697167e-04 3.4158094975963397e-04
108 107 3.37464595092842989 1.9942109762809311e-04 2.0596419432700153e-04
109 108 3.52803894869790380 1.1632897361638936e-04 1.2130288201060519e-04
110 109 3.68143194646737770 6.6168773983632875e-05 6.9780136964352985e-05
111 110 3.83482494423685205 3.6693592845468994e-05 3.9207921690589931e-05
112 111 3.98821794200632596 1.9834374511064674e-05 2.1517763650859156e-05
113 112 4.14161093977580030 1.0448465144221465e-05 1.1534579060157566e-05
114 113 4.29500393754527376 5.3629290120784096e-06 6.0393148798809450e-06
115 114 4.44839693531474811 2.6814645060391950e-06 3.0885518982983557e-06
116 115 4.60178993308422246 1.3057566290277394e-06 1.5427780080438974e-06
117 116 4.75518293085369681 6.1910874652178859e-07 7.5271969901508153e-07
118 117 4.90857592862317027 2.8574249839467164e-07 3.5871078186222288e-07
119 118 5.06196892639264462 1.2834196961794589e-07 1.6696939963261641e-07
120 119 5.21536192416211897 5.6082205211203769e-08 7.5912037280779167e-08
121 120 5.36875492193159243 2.3834937214761211e-08 3.3710540397483414e-08
122 121 5.52214791970106678 9.8491476094055301e-09 1.4621842059507159e-08
123 122 5.67554091747054112 3.9558051873841431e-09 6.1946927217086197e-09
124 123 5.82893391524001458 1.5437288536133231e-09 2.5634140201581425e-09
125 124 5.98232691300948893 5.8512303322440968e-10 1.0360937362164591e-09
126 125 6.13571991077896328 2.1532527622657907e-10 4.0903516608474877e-10
127 126 6.28911290854843674 7.6901884366636397e-11 1.5772609560369330e-10
128 127 6.44250590631791109 2.6643172536471990e-11 5.9405651698871143e-11
129 128 6.59589890408738544 8.9504407739712559e-12 2.1854117949406021e-11
130 129 6.74929190185685979 2.9140969961766280e-12 7.8527199052172838e-12
131 130 6.90268489962633325 9.1906136033265523e-13 2.7560572698411681e-12
132 131 7.05607789739580760 2.8062942300233449e-13 9.4479519267978745e-13
133 132 7.20947089516528195 8.2913238614324415e-14 3.1635042202076297e-13
134 133 7.36286389293475541 2.3689496746950673e-14 1.0346190432549043e-13
135 134 7.51625689070422975 6.5411296987848212e-15 3.3050179591336516e-14
136 135 7.66964988847370410 1.7443012530093037e-15 1.0312132532960704e-14
137 136 7.82304288624317756 4.4890105775973291e-16 3.1427110644852564e-15
138 137 7.97643588401265191 1.1140610192577334e-16 9.3549555743936295e-16
139 138 8.12982888178212626 2.6640589590945988e-17 2.7199461796138341e-16
140 139 8.28322187955160061 6.1330853734552610e-18 7.7243189477036549e-17
141 140 8.43661487732107496 1.3580403326936764e-18 2.1426014371814620e-17
142 141 8.59000787509054753 2.8894475163695049e-19 5.8050222942283077e-18
143 142 8.74340087286002188 5.9009843644165918e-20 1.5361997793645551e-18
144 143 8.89679387062949623 1.1554374979277373e-20 3.9707524370429841e-19
145 144 9.05018686839897057 2.1664453086144553e-21 1.0024881094659756e-19
146 145 9.20357986616844492 3.8846605533776366e-22 2.4721052418186992e-20
147 146 9.35697286393791927 6.6518160160576584e-23 5.9543723204776714e-21
148 147 9.51036586170739362 1.0860107781318568e-23 1.4008328742913487e-21
149 148 9.66375885947686619 1.6877194525022136e-24 3.2189777095440539e-22
150 149 9.81715185724634054 2.4919347620837903e-25 7.2248846868644842e-23
151 150 9.97054485501581489 3.4887086669172374e-26 1.5838905832131320e-23
152 151 10.12393785278528924 4.6208061813474098e-27 3.3915696477242618e-24
153 152 10.27733085055476359 5.7760077266841887e-28 7.0934515943270875e-25
154 153 10.43072384832423793 6.7953032078638413e-29 1.4490914207904825e-25
155 154 10.58411684609371051 7.5013087359536756e-30 2.8914472079863166e-26
156 155 10.73750984386318486 7.7432864371137072e-31 5.6352872156522522e-27
157 156 10.89090284163265920 7.4454677279937877e-32 1.0727490794078742e-27
158 157 11.04429583940213355 6.6392705854720298e-33 1.9946263479627000e-28
159 158 11.19768883717160790 5.4626909880467249e-34 3.6224821896093798e-29
160 159 11.35108183494108225 4.1227856513559951e-35 6.4258749910530849e-30
161 160 11.50447483271055660 2.8344151353071975e-36 1.1133701987435749e-30
162 161 11.65786783048002917 1.7605062952218917e-37 1.8842052899791108e-31
163 162 11.81126082824950352 9.7805905290106760e-39 3.1145703961477821e-32
164 163 11.96465382601897787 4.8002898301891583e-40 5.0286266217181697e-33
165 164 12.11804682378845222 2.0489041958124106e-41 7.9301597373135953e-34
166 165 12.27143982155792656 7.4505607120452671e-43 1.2215065128760695e-34
167 166 12.42483281932740091 2.2441447927847241e-44 1.8377690984236611e-35
168 167 12.57822581709687348 5.3751971084665718e-46 2.7006444336879435e-36
169 168 12.73161881486634783 9.5985662651187374e-48 3.8763696021741189e-37
170 169 12.88501181263582218 1.1359250017892029e-49 5.4345583489117509e-38
171 170 13.03840481040529653 6.6819117752305559e-52 7.4419138643607013e-39
Difference
1 7.4419138643600331e-39
2 5.4345583489003916e-38
3 3.8763696020781333e-37
4 2.7006444331504238e-36
5 1.8377690961795164e-35
6 1.2215065054255088e-34
7 7.9301595324231765e-34
8 5.0286261416891864e-33
9 3.1145694180887292e-32
10 1.8842035294728156e-31
11 1.1133673643284396e-30
12 6.4258337631965715e-30
13 3.6224275626994994e-29
14 1.9945599552568454e-28
15 1.0726746247305942e-27
16 5.6345128870085410e-27
17 2.8906970771127210e-26
18 1.4484118904696962e-25
19 7.0876755866004035e-25
20 3.3869488415429145e-24
21 1.5804018745462147e-23
22 7.1999653392436462e-23
23 3.2021005150190317e-22
24 1.3899727665100302e-21
25 5.8878541603170950e-21
26 2.4332586362849229e-20
27 9.8082365637983105e-20
28 3.8552086872502105e-19
29 1.4771899357203892e-18
30 5.5160775425913572e-18
31 2.0067974039120942e-17
32 7.1110104103581292e-17
33 2.4535402837043726e-16
34 8.2408945551358961e-16
35 2.6938100067255235e-15
36 8.5678312799514006e-15
37 2.6509049892551695e-14
38 7.9772407578539758e-14
39 2.3343718340643886e-13
40 6.6416576967745300e-13
41 1.8369959095085126e-12
42 4.9386229090406554e-12
43 1.2903677175434765e-11
44 3.2762479162399156e-11
45 8.0824211237056903e-11
46 1.9370988985816970e-10
47 4.5097070299204944e-10
48 1.0196851665448194e-09
49 2.2388875343244765e-09
50 4.7726944501016292e-09
51 9.8756031827222032e-09
52 1.9829832069575398e-08
53 3.8627430014670522e-08
54 7.2968283467551244e-08
55 1.3361095249329293e-07
56 2.3702137901615796e-07
57 4.0708739225916063e-07
58 6.7638586780253542e-07
59 1.0861139159361013e-06
60 1.6833891397944817e-06
61 2.5143288451209370e-06
62 3.6113629807201100e-06
63 4.9739083942158271e-06
64 6.5430966989084240e-06
65 8.1738021626622946e-06
66 9.6105119739789023e-06
67 1.0476874667792119e-05
68 1.0290784383833098e-05
69 8.5160136535184991e-06
70 4.6562541589846747e-06
71 1.6126149070243984e-06
72 1.0290116337820059e-05
73 2.0911425934425076e-05
74 3.2463774016402991e-05
75 4.3403626364974662e-05
76 5.1806607120463005e-05
77 5.5654830360386820e-05
78 5.3228590801153441e-05
79 4.3530553367657210e-05
80 2.6643151714883517e-05
81 3.9156714092131173e-06
82 2.2096950048663966e-05
83 4.7968440318971184e-05
84 6.9964700619089271e-05
85 8.4727253321537077e-05
86 8.9925920160827122e-05
87 8.4727253321537077e-05
88 6.9964700619089271e-05
89 4.7968440318971184e-05
90 2.2096950048643149e-05
91 3.9156714091992395e-06
92 2.6643151714897395e-05
93 4.3530553367657210e-05
94 5.3228590801153441e-05
95 5.5654830360386820e-05
96 5.1806607120456066e-05
97 4.3403626364974662e-05
98 3.2463774016392583e-05
99 2.0911425934425076e-05
100 1.0290116337820059e-05
101 1.6126149070243984e-06
102 4.6562541589846747e-06
103 8.5160136535184991e-06
104 1.0290784383834399e-05
105 1.0476874667792119e-05
106 9.6105119739789023e-06
107 8.1738021626622946e-06
108 6.5430966989084240e-06
109 4.9739083942158271e-06
110 3.6113629807201100e-06
111 2.5143288451209370e-06
112 1.6833891397944817e-06
113 1.0861139159361013e-06
114 6.7638586780253542e-07
115 4.0708739225916063e-07
116 2.3702137901615796e-07
117 1.3361095249329293e-07
118 7.2968283467551244e-08
119 3.8627430014670522e-08
120 1.9829832069575398e-08
121 9.8756031827222032e-09
122 4.7726944501016292e-09
123 2.2388875343244765e-09
124 1.0196851665448194e-09
125 4.5097070299204944e-10
126 1.9370988985816970e-10
127 8.0824211237056903e-11
128 3.2762479162399156e-11
129 1.2903677175434765e-11
130 4.9386229090406554e-12
131 1.8369959095085126e-12
132 6.6416576967745300e-13
133 2.3343718340643855e-13
134 7.9772407578539758e-14
135 2.6509049892551695e-14
136 8.5678312799514006e-15
137 2.6938100067255235e-15
138 8.2408945551358961e-16
139 2.4535402837043740e-16
140 7.1110104103581292e-17
141 2.0067974039120942e-17
142 5.5160775425913572e-18
143 1.4771899357203892e-18
144 3.8552086872502105e-19
145 9.8082365637983105e-20
146 2.4332586362849229e-20
147 5.8878541603170950e-21
148 1.3899727665100302e-21
149 3.2021005150190317e-22
150 7.1999653392436462e-23
151 1.5804018745462147e-23
152 3.3869488415429145e-24
153 7.0876755866004035e-25
154 1.4484118904696962e-25
155 2.8906970771127210e-26
156 5.6345128870085410e-27
157 1.0726746247305942e-27
158 1.9945599552568454e-28
159 3.6224275626994994e-29
160 6.4258337631965715e-30
161 1.1133673643284396e-30
162 1.8842035294728156e-31
163 3.1145694180887292e-32
164 5.0286261416891864e-33
165 7.9301595324231765e-34
166 1.2215065054255088e-34
167 1.8377690961795164e-35
168 2.7006444331504238e-36
169 3.8763696020781333e-37
170 5.4345583489003916e-38
171 7.4419138643600331e-39
m x PBinomial TPoisson
1 0 -0.58195992534659879 7.1295394683814373e-01 7.1319528789828224e-01
2 1 1.13981500171434424 2.4146135674478209e-01 2.4106000730961941e-01
3 2 2.86158992877528728 4.0646801536195799e-02 4.0739141235325689e-02
4 3 4.58336485583623077 4.5344127298227776e-03 4.5899432458466945e-03
5 4 6.30513978289717336 3.7711047753035131e-04 3.8785020427404605e-04
6 5 8.02691470995811684 2.4939169856716626e-05 2.6218673808925528e-05
7 6 9.74868963701906033 1.3660734323652354e-06 1.4769852912361330e-06
8 7 11.47046456408000381 6.3747486251226370e-08 7.1317289776830584e-08
9 8 13.19223949114094552 2.5869470873493718e-09 3.0131554930710899e-09
10 9 14.91401441820189078 9.2740699412880757e-11 1.1316072851755880e-10
11 10 16.63578934526283248 2.9736496805733343e-12 3.8248326238934915e-12
12 11 18.35756427232377774 8.6137784516516593e-14 1.1752667517054522e-13
13 12 20.07933919938471945 2.2728406736155061e-15 3.3103346839703447e-15
14 13 21.80111412644566471 5.5007859682077003e-17 8.6068701783229011e-17
15 14 23.52288905350660642 1.2283461366166612e-18 2.0779443716236707e-18
16 15 25.24466398056754812 2.5436693543832143e-20 4.6823013173920516e-20
17 16 26.96643890762849338 4.9063762597070969e-22 9.8913615329906107e-22
18 17 28.68821383468943154 8.8491756187102855e-24 1.9666354106769770e-23
19 18 30.40998876175037680 1.4975224827922158e-25 3.6929042711601057e-25
20 19 32.13176368881131850 2.3850426632383229e-27 6.5694823350112188e-27
21 20 33.85353861587226021 3.5847334617810187e-29 1.1102425146168887e-28
22 21 35.57531354293320902 5.0971016872351015e-31 1.7869617616214588e-30
23 22 37.29708846999415073 6.8716619576499106e-33 2.7454230701275129e-32
24 23 39.01886339705509243 8.8013793480397743e-35 4.0345782508830377e-34
25 24 40.74063832411603414 1.0729804482413077e-36 5.6820310366602559e-36
26 25 42.46241325117697585 1.2471516232063543e-38 7.6821059615647506e-38
27 26 44.18418817823792466 1.3842287169856084e-40 9.9867377500340474e-40
28 27 45.90596310529886637 1.4691954763522991e-42 1.2501916146339190e-41
29 28 47.62773803235980807 1.4931703238049465e-44 1.5091598776652069e-43
30 29 49.34951295942074978 1.4548891967140725e-46 1.7589518574166675e-45
31 30 51.07128788648169149 1.3606178192382870e-48 1.9817524260228065e-47
32 31 52.79306281354264030 1.2226121719188214e-50 2.1607494193410234e-49
33 32 54.51483774060358201 1.0566162307414568e-52 2.2822915741788962e-51
34 33 56.23661266766452371 8.7906979784768393e-55 2.3376198547650520e-53
35 34 57.95838759472546542 7.0466516861539606e-57 2.3238691497370288e-55
36 35 59.68016252178640713 5.4468822080203255e-59 2.2441936360317592e-57
37 36 61.40193744884735594 4.0630272538118696e-61 2.1070484693854402e-59
38 37 63.12371237590829764 2.9268408425335054e-63 1.9248172504115114e-61
39 38 64.84548730296923225 2.0374590824513826e-65 1.7120742911555187e-63
40 39 66.56726223003018106 1.3714975581991044e-67 1.4837977190014719e-65
41 40 68.28903715709112987 8.9325993269477906e-70 1.2538090725562195e-67
42 41 70.01081208415206447 5.6322660598088978e-72 1.0336279671317201e-69
43 42 71.73258701121301328 3.4398800250764738e-74 8.3182441164408668e-72
44 43 73.45436193827396210 2.0360011333584289e-76 6.5385267705977097e-74
45 44 75.17613686533489670 1.1684101967715374e-78 5.0227773828682694e-76
46 45 76.89791179239584551 6.5041761120663088e-81 3.7726639009100899e-78
47 46 78.61968671945678011 3.5136265482974304e-83 2.7720878228425260e-80
48 47 80.34146164651772892 1.8427325520853704e-85 1.9935440087676496e-82
49 48 82.06323657357867773 9.3859957980299616e-88 1.4037872395071754e-84
50 49 83.78501150063961234 4.6448222631453378e-90 9.6832670806824604e-87
51 50 85.50678642770056115 2.2339826516129709e-92 6.5458885465412674e-89
52 51 87.22856135476149575 1.0446144663520809e-94 4.3382555465312595e-91
53 52 88.95033628182244456 4.7504434649891129e-97 2.8198661052451669e-93
54 53 90.67211120888339337 2.1015687427827360e-99 1.7983297048544875e-95
55 54 92.39388613594432798 9.0470561182660932e-102 1.1256211856311731e-97
56 55 94.11566106300527679 3.7908961690675605e-104 6.9174538316971115e-100
57 56 95.83743599006621139 1.5465293561182732e-106 4.1751774912741595e-102
58 57 97.55921091712716020 6.1441415195786571e-109 2.4758070035977418e-104
59 58 99.28098584418810901 2.3776651585681547e-111 1.4427978745103320e-106
60 59 101.00276077124904361 8.9643976971255313e-114 8.2655200268561848e-109
61 60 102.72453569830999243 3.2935328880552956e-116 4.6562429484621330e-111
62 61 104.44631062537092703 1.1793918486088320e-118 2.5800165845577007e-113
63 62 106.16808555243187584 4.1170831873345288e-121 1.4065251702911503e-115
64 63 107.88986047949282465 1.4013038809198887e-123 7.5461191675943544e-118
65 64 109.61163540655375925 4.6511213482433911e-126 3.9852941853854034e-120
66 65 111.33341033361472228 1.5056813367212981e-128 2.0723529764004202e-122
67 66 113.05518526067565688 4.7546869198704179e-131 1.0612959182171539e-124
68 67 114.77696018773660569 1.4648184510712281e-133 5.3540003038420438e-127
69 68 116.49873511479754029 4.4032618769677607e-136 2.6612530922038499e-129
70 69 118.22051004185848910 1.2916541766830431e-138 1.3036283263259568e-131
71 70 119.94228496891943792 3.6978361771631915e-141 6.2946624899735414e-134
72 71 121.66405989598037252 1.0332941419152619e-143 2.9966139741002665e-136
73 72 123.38583482304132133 2.8184932617373990e-146 1.4067437822859853e-138
74 73 125.10760975010225593 7.5052528725538133e-149 6.5134164166112894e-141
75 74 126.82938467716320474 1.9512112759713333e-151 2.9750469578576382e-143
76 75 128.55115960422415355 4.9529745148232785e-154 1.3407544956745258e-145
77 76 130.27293453128510237 1.2276648148754765e-156 5.9628292044472776e-148
78 77 131.99470945834602276 2.9714709362471615e-159 2.6174497027313843e-150
79 78 133.71648438540697157 7.0236710892228204e-162 1.1342282045169369e-152
80 79 135.43825931246792038 1.6213542759425012e-164 4.8527738370472831e-155
81 80 137.16003423952886919 3.6553578365438102e-167 2.0502969461523259e-157
82 81 138.88180916658981801 8.0488593842593791e-170 8.5555600962903860e-160
83 82 140.60358409365073840 1.7310221071775125e-172 3.5265601372514317e-162
84 83 142.32535902071168721 3.6361620427464505e-175 1.4361172607119528e-164
85 84 144.04713394777263602 7.4603954498570929e-178 5.7786623109599818e-167
86 85 145.76890887483358483 1.4950692284283295e-180 2.2978680718877476e-169
87 86 147.49068380189453364 2.9264532597281899e-183 9.0311559104424910e-172
88 87 149.21245872895545403 5.5949973638642417e-186 3.5086559744018878e-174
89 88 150.93423365601640285 1.0447936414575886e-188 1.3476428628952444e-176
90 89 152.65600858307735166 1.9055703532474168e-191 5.1180144680740569e-179
91 90 154.37778351013830047 3.3944695671296323e-194 1.9220987668990676e-181
92 91 156.09955843719924928 5.9055054241055213e-197 7.1392239913385361e-184
93 92 157.82133336426016967 1.0033750611664154e-199 2.6228888142092566e-186
94 93 159.54310829132111849 1.6648324543670474e-202 9.5326496688465730e-189
95 94 161.26488321838206730 2.6974644295379735e-205 3.4276974341174321e-191
96 95 162.98665814544301611 4.2676897419123841e-208 1.2195386660333770e-193
97 96 164.70843307250396492 6.5925400989784532e-211 4.2937923866586899e-196
98 97 166.43020799956488531 9.9426776692659444e-214 1.4961874501966308e-198
99 98 168.15198292662583412 1.4638926673493116e-216 5.1603199812904305e-201
100 99 169.87375785368678294 2.1039327013990397e-219 1.7618062158346538e-203
101 100 171.59553278074773175 2.9514085991567122e-222 5.9549050095210550e-206
102 101 173.31730770780868056 4.0406990881130015e-225 1.9928295972456394e-208
103 102 175.03908263486960095 5.3983955753011828e-228 6.6036902340097351e-211
104 103 176.76085756193054976 7.0372298683804655e-231 2.1670362127138242e-213
105 104 178.48263248899149858 8.9497682155296332e-234 7.0428676913198811e-216
106 105 180.20440741605244739 1.1102871152007615e-236 2.2671326473011088e-218
107 106 181.92618234311339620 1.3434108854094848e-239 7.2291588187528861e-221
108 107 183.64795727017431659 1.5851307433708658e-242 2.2836034399423887e-223
109 108 185.36973219723526540 1.8236121518776116e-245 7.1468329879676494e-226
110 109 187.09150712429621422 2.0451975743143419e-248 2.2161738990213939e-228
111 110 188.81328205135716303 2.2355958181610869e-251 6.8096979806288696e-231
112 111 190.53505697841811184 2.3813420222701466e-254 2.0735837094169441e-233
113 112 192.25683190547903223 2.4713326168702070e-257 6.2577794087756504e-236
114 113 193.97860683253998104 2.4981992154509250e-260 1.8717959647488328e-238
115 114 195.70038175960092985 2.4592897385163636e-263 5.5497108428518552e-241
116 115 197.42215668666187867 2.3570782542198674e-266 1.6311324042468917e-243
117 116 199.14393161372282748 2.1989189711815151e-269 4.7527823503061110e-246
118 117 200.86570654078374787 1.9961753502320978e-272 1.3730260123103980e-248
119 118 202.58748146784469668 1.7628667200854020e-275 3.9329050183130713e-251
120 119 204.30925639490564549 1.5140567306774944e-278 1.1170772236889445e-253
121 120 206.03103132196659431 1.2642424270856616e-281 3.1464341800572820e-256
122 121 207.75280624902754312 1.0259838507956551e-284 8.7892128335476567e-259
123 122 209.47458117608846351 8.0894945363161663e-288 2.4350442112614873e-261
124 123 211.19635610314941232 6.1946045457891402e-291 6.6914223041171918e-264
125 124 212.91813103021036113 4.6052073357406957e-294 1.8239522087029551e-266
126 125 214.63990595727130994 3.3223940698734168e-297 4.9319667723328993e-269
127 126 216.36168088433225876 2.3250523121547522e-300 1.3230196579750735e-271
128 127 218.08345581139317915 1.5776000729438210e-303 3.5211074361859257e-274
129 128 219.80523073845412796 1.0373747974640787e-306 9.2979243236764388e-277
130 129 221.52700566551507677 6.6073801395081404e-310 2.4362003266688824e-279
131 130 223.24878059257602558 4.0742285429399163e-313 6.3341208493388278e-282
132 131 224.97055551963697440 2.4307380079065049e-316 1.6342998832645627e-284
133 132 226.69233044669789479 1.4023065225912101e-319 4.1847981859347369e-287
134 133 228.41410537375884360 7.9050503334599447e-323 1.0635051028918303e-289
135 134 230.13588030081979241 0.0000000000000000e+00 2.6825725729655712e-292
136 135 231.85765522788074122 0.0000000000000000e+00 6.7163668863887429e-295
137 136 233.57943015494169003 0.0000000000000000e+00 1.6692147114701774e-297
138 137 235.30120508200261042 0.0000000000000000e+00 4.1182085582257929e-300
139 138 237.02298000906355924 0.0000000000000000e+00 1.0086626758551560e-302
140 139 238.74475493612450805 0.0000000000000000e+00 2.4527193125111484e-305
141 140 240.46652986318545686 0.0000000000000000e+00 5.9215651973487318e-308
142 141 242.18830479024640567 0.0000000000000000e+00 1.4194957707119193e-310
143 142 243.91007971730732606 0.0000000000000000e+00 3.3787997922713783e-313
144 143 245.63185464436827488 0.0000000000000000e+00 7.9862540736922495e-316
145 144 247.35362957142922369 0.0000000000000000e+00 1.8745492888556488e-318
146 145 249.07540449849017250 0.0000000000000000e+00 4.3675403092366195e-321
147 146 250.79717942555112131 0.0000000000000000e+00 9.8813129168249309e-324
148 147 252.51895435261204170 0.0000000000000000e+00 0.0000000000000000e+00
149 148 254.24072927967299051 0.0000000000000000e+00 0.0000000000000000e+00
150 149 255.96250420673393933 0.0000000000000000e+00 0.0000000000000000e+00
151 150 257.68427913379485972 0.0000000000000000e+00 0.0000000000000000e+00
152 151 259.40605406085580853 0.0000000000000000e+00 0.0000000000000000e+00
153 152 261.12782898791675734 0.0000000000000000e+00 0.0000000000000000e+00
154 153 262.84960391497770615 0.0000000000000000e+00 0.0000000000000000e+00
155 154 264.57137884203865497 0.0000000000000000e+00 0.0000000000000000e+00
156 155 266.29315376909960378 0.0000000000000000e+00 0.0000000000000000e+00
157 156 268.01492869616055259 0.0000000000000000e+00 0.0000000000000000e+00
158 157 269.73670362322150140 0.0000000000000000e+00 0.0000000000000000e+00
159 158 271.45847855028245021 0.0000000000000000e+00 0.0000000000000000e+00
160 159 273.18025347734339903 0.0000000000000000e+00 0.0000000000000000e+00
161 160 274.90202840440429100 0.0000000000000000e+00 0.0000000000000000e+00
162 161 276.62380333146523981 0.0000000000000000e+00 0.0000000000000000e+00
163 162 278.34557825852618862 0.0000000000000000e+00 0.0000000000000000e+00
164 163 280.06735318558713743 0.0000000000000000e+00 0.0000000000000000e+00
165 164 281.78912811264808624 0.0000000000000000e+00 0.0000000000000000e+00
166 165 283.51090303970903506 0.0000000000000000e+00 0.0000000000000000e+00
167 166 285.23267796676998387 0.0000000000000000e+00 0.0000000000000000e+00
168 167 286.95445289383093268 0.0000000000000000e+00 0.0000000000000000e+00
169 168 288.67622782089188149 0.0000000000000000e+00 0.0000000000000000e+00
170 169 290.39800274795283030 0.0000000000000000e+00 0.0000000000000000e+00
Difference1 TLocal Difference2
1 2.4134106013851131e-04 5.7988729257321758e-01 1.3306665426492614e-01
2 4.0134943516267896e-04 3.5873477236220347e-01 1.1727341561742138e-01
3 9.2339699129889707e-05 1.1448102304068192e-02 2.9198699232127607e-02
4 5.5530516023916988e-05 1.8846194627465117e-05 4.5155665351953121e-03
5 1.0739726743694744e-05 1.6004569078579256e-09 3.7710887707344346e-04
6 1.2795039522089013e-06 7.0112336811908773e-15 2.4939169849705392e-05
7 1.1091185887089757e-07 1.5844372441809378e-21 1.3660734323652339e-06
8 7.5698035256042140e-09 1.8470803417829573e-29 6.3747486251226370e-08
9 4.2620840572171813e-10 1.1107764750536744e-38 2.5869470873493718e-09
10 2.0420029104678042e-11 3.4458605959779781e-49 9.2740699412880757e-11
11 8.5118294332015719e-13 5.5144077750200545e-61 2.9736496805733343e-12
12 3.1388890654028626e-14 4.5522928776651959e-74 8.6137784516516593e-14
13 1.0374940103548386e-15 1.9386153892610541e-88 2.2728406736155061e-15
14 3.1060842101152008e-17 4.2587609199326902e-104 5.5007859682077003e-17
15 8.4959823500700957e-19 4.8261965822649502e-121 1.2283461366166612e-18
16 2.1386319630088373e-20 2.8213495665489936e-139 2.5436693543832143e-20
17 4.9849852732835139e-22 8.5082243518188135e-159 4.9063762597070969e-22
18 1.0817178488059485e-23 1.3235827884358059e-179 8.8491756187102855e-24
19 2.1953817883678901e-25 1.0621685357493945e-201 1.4975224827922158e-25
20 4.1844396717728959e-27 4.3970954886414686e-225 2.3850426632383229e-27
21 7.5176916843878684e-29 9.3900629788878500e-250 3.5847334617810187e-29
22 1.2772515928979485e-30 1.0344303557034564e-275 5.0971016872351015e-31
23 2.0582568743625217e-32 5.8784679062116810e-303 6.8716619576499106e-33
24 3.1544403160790603e-34 0.0000000000000000e+00 8.8013793480397743e-35
25 4.6090505884189479e-36 0.0000000000000000e+00 1.0729804482413077e-36
26 6.4349543383583960e-38 0.0000000000000000e+00 1.2471516232063543e-38
27 8.6025090330484393e-40 0.0000000000000000e+00 1.3842287169856084e-40
28 1.1032720669986891e-41 0.0000000000000000e+00 1.4691954763522991e-42
29 1.3598428452847122e-43 0.0000000000000000e+00 1.4931703238049465e-44
30 1.6134629377452603e-45 0.0000000000000000e+00 1.4548891967140725e-46
31 1.8456906440989777e-47 0.0000000000000000e+00 1.3606178192382870e-48
32 2.0384882021491412e-49 0.0000000000000000e+00 1.2226121719188214e-50
33 2.1766299511047504e-51 0.0000000000000000e+00 1.0566162307414568e-52
34 2.2497128749802834e-53 0.0000000000000000e+00 8.7906979784768393e-55
35 2.2534026328754891e-55 0.0000000000000000e+00 7.0466516861539606e-57
36 2.1897248139515560e-57 0.0000000000000000e+00 5.4468822080203255e-59
37 2.0664181968473213e-59 0.0000000000000000e+00 4.0630272538118696e-61
38 1.8955488419861765e-61 0.0000000000000000e+00 2.9268408425335054e-63
39 1.6916997003310049e-63 0.0000000000000000e+00 2.0374590824513826e-65
40 1.4700827434194809e-65 0.0000000000000000e+00 1.3714975581991044e-67
41 1.2448764732292717e-67 0.0000000000000000e+00 8.9325993269477906e-70
42 1.0279957010719112e-69 0.0000000000000000e+00 5.6322660598088978e-72
43 8.2838453161901023e-72 0.0000000000000000e+00 3.4398800250764738e-74
44 6.5181667592641252e-74 0.0000000000000000e+00 2.0360011333584289e-76
45 5.0110932809005543e-76 0.0000000000000000e+00 1.1684101967715374e-78
46 3.7661597247980236e-78 0.0000000000000000e+00 6.5041761120663088e-81
47 2.7685741962942284e-80 0.0000000000000000e+00 3.5136265482974304e-83
48 1.9917012762155642e-82 0.0000000000000000e+00 1.8427325520853704e-85
49 1.4028486399273725e-84 0.0000000000000000e+00 9.3859957980299616e-88
50 9.6786222584193142e-87 0.0000000000000000e+00 4.6448222631453378e-90
51 6.5436545638896549e-89 0.0000000000000000e+00 2.2339826516129709e-92
52 4.3372109320649076e-91 0.0000000000000000e+00 1.0446144663520809e-94
53 2.8193910608986678e-93 0.0000000000000000e+00 4.7504434649891129e-97
54 1.7981195479802091e-95 0.0000000000000000e+00 2.1015687427827360e-99
55 1.1255307150699905e-97 0.0000000000000000e+00 9.0470561182660932e-102
56 6.9170747420802045e-100 0.0000000000000000e+00 3.7908961690675605e-104
57 4.1750228383385473e-102 0.0000000000000000e+00 1.5465293561182732e-106
58 2.4757455621825459e-104 0.0000000000000000e+00 6.1441415195786571e-109
59 1.4427740978587462e-106 0.0000000000000000e+00 2.3776651585681547e-111
60 8.2654303828792133e-109 0.0000000000000000e+00 8.9643976971255313e-114
61 4.6562100131332522e-111 0.0000000000000000e+00 3.2935328880552956e-116
62 2.5800047906392146e-113 0.0000000000000000e+00 1.1793918486088320e-118
63 1.4065210532079629e-115 0.0000000000000000e+00 4.1170831873345288e-121
64 7.5461051545555448e-118 0.0000000000000000e+00 1.4013038809198887e-123
65 3.9852895342640549e-120 0.0000000000000000e+00 4.6511213482433911e-126
66 2.0723514707190835e-122 0.0000000000000000e+00 1.5056813367212981e-128
67 1.0612954427484620e-124 0.0000000000000000e+00 4.7546869198704179e-131
68 5.3539988390235931e-127 0.0000000000000000e+00 1.4648184510712281e-133
69 2.6612526518776622e-129 0.0000000000000000e+00 4.4032618769677607e-136
70 1.3036281971605391e-131 0.0000000000000000e+00 1.2916541766830431e-138
71 6.2946621201899238e-134 0.0000000000000000e+00 3.6978361771631915e-141
72 2.9966138707708524e-136 0.0000000000000000e+00 1.0332941419152619e-143
73 1.4067437541010526e-138 0.0000000000000000e+00 2.8184932617373990e-146
74 6.5134163415587606e-141 0.0000000000000000e+00 7.5052528725538133e-149
75 2.9750469383455254e-143 0.0000000000000000e+00 1.9512112759713333e-151
76 1.3407544907215512e-145 0.0000000000000000e+00 4.9529745148232785e-154
77 5.9628291921706296e-148 0.0000000000000000e+00 1.2276648148754765e-156
78 2.6174496997599134e-150 0.0000000000000000e+00 2.9714709362471615e-159
79 1.1342282038145698e-152 0.0000000000000000e+00 7.0236710892228204e-162
80 4.8527738354259285e-155 0.0000000000000000e+00 1.6213542759425012e-164
81 2.0502969457867903e-157 0.0000000000000000e+00 3.6553578365438102e-167
82 8.5555600954854999e-160 0.0000000000000000e+00 8.0488593842593791e-170
83 3.5265601370783294e-162 0.0000000000000000e+00 1.7310221071775125e-172
84 1.4361172606755911e-164 0.0000000000000000e+00 3.6361620427464505e-175
85 5.7786623108853783e-167 0.0000000000000000e+00 7.4603954498570929e-178
86 2.2978680718727968e-169 0.0000000000000000e+00 1.4950692284283295e-180
87 9.0311559104132270e-172 0.0000000000000000e+00 2.9264532597281899e-183
88 3.5086559743962930e-174 0.0000000000000000e+00 5.5949973638642417e-186
89 1.3476428628941996e-176 0.0000000000000000e+00 1.0447936414575886e-188
90 5.1180144680721514e-179 0.0000000000000000e+00 1.9055703532474168e-191
91 1.9220987668987281e-181 0.0000000000000000e+00 3.3944695671296323e-194
92 7.1392239913379456e-184 0.0000000000000000e+00 5.9055054241055213e-197
93 2.6228888142091561e-186 0.0000000000000000e+00 1.0033750611664154e-199
94 9.5326496688464072e-189 0.0000000000000000e+00 1.6648324543670474e-202
95 3.4276974341174053e-191 0.0000000000000000e+00 2.6974644295379735e-205
96 1.2195386660333727e-193 0.0000000000000000e+00 4.2676897419123841e-208
97 4.2937923866586832e-196 0.0000000000000000e+00 6.5925400989784532e-211
98 1.4961874501966299e-198 0.0000000000000000e+00 9.9426776692659444e-214
99 5.1603199812904291e-201 0.0000000000000000e+00 1.4638926673493116e-216
100 1.7618062158346535e-203 0.0000000000000000e+00 2.1039327013990397e-219
101 5.9549050095210550e-206 0.0000000000000000e+00 2.9514085991567122e-222
102 1.9928295972456394e-208 0.0000000000000000e+00 4.0406990881130015e-225
103 6.6036902340097351e-211 0.0000000000000000e+00 5.3983955753011828e-228
104 2.1670362127138242e-213 0.0000000000000000e+00 7.0372298683804655e-231
105 7.0428676913198811e-216 0.0000000000000000e+00 8.9497682155296332e-234
106 2.2671326473011088e-218 0.0000000000000000e+00 1.1102871152007615e-236
107 7.2291588187528861e-221 0.0000000000000000e+00 1.3434108854094848e-239
108 2.2836034399423887e-223 0.0000000000000000e+00 1.5851307433708658e-242
109 7.1468329879676494e-226 0.0000000000000000e+00 1.8236121518776116e-245
110 2.2161738990213939e-228 0.0000000000000000e+00 2.0451975743143419e-248
111 6.8096979806288696e-231 0.0000000000000000e+00 2.2355958181610869e-251
112 2.0735837094169441e-233 0.0000000000000000e+00 2.3813420222701466e-254
113 6.2577794087756504e-236 0.0000000000000000e+00 2.4713326168702070e-257
114 1.8717959647488328e-238 0.0000000000000000e+00 2.4981992154509250e-260
115 5.5497108428518552e-241 0.0000000000000000e+00 2.4592897385163636e-263
116 1.6311324042468917e-243 0.0000000000000000e+00 2.3570782542198674e-266
117 4.7527823503061110e-246 0.0000000000000000e+00 2.1989189711815151e-269
118 1.3730260123103980e-248 0.0000000000000000e+00 1.9961753502320978e-272
119 3.9329050183130713e-251 0.0000000000000000e+00 1.7628667200854020e-275
120 1.1170772236889445e-253 0.0000000000000000e+00 1.5140567306774944e-278
121 3.1464341800572820e-256 0.0000000000000000e+00 1.2642424270856616e-281
122 8.7892128335476567e-259 0.0000000000000000e+00 1.0259838507956551e-284
123 2.4350442112614873e-261 0.0000000000000000e+00 8.0894945363161663e-288
124 6.6914223041171918e-264 0.0000000000000000e+00 6.1946045457891402e-291
125 1.8239522087029551e-266 0.0000000000000000e+00 4.6052073357406957e-294
126 4.9319667723328993e-269 0.0000000000000000e+00 3.3223940698734168e-297
127 1.3230196579750735e-271 0.0000000000000000e+00 2.3250523121547522e-300
128 3.5211074361859257e-274 0.0000000000000000e+00 1.5776000729438210e-303
129 9.2979243236764388e-277 0.0000000000000000e+00 1.0373747974640787e-306
130 2.4362003266688824e-279 0.0000000000000000e+00 6.6073801395081404e-310
131 6.3341208493388278e-282 0.0000000000000000e+00 4.0742285429399163e-313
132 1.6342998832645627e-284 0.0000000000000000e+00 2.4307380079065049e-316
133 4.1847981859347369e-287 0.0000000000000000e+00 1.4023065225912101e-319
134 1.0635051028918303e-289 0.0000000000000000e+00 7.9050503334599447e-323
135 2.6825725729655712e-292 0.0000000000000000e+00 0.0000000000000000e+00
136 6.7163668863887429e-295 0.0000000000000000e+00 0.0000000000000000e+00
137 1.6692147114701774e-297 0.0000000000000000e+00 0.0000000000000000e+00
138 4.1182085582257929e-300 0.0000000000000000e+00 0.0000000000000000e+00
139 1.0086626758551560e-302 0.0000000000000000e+00 0.0000000000000000e+00
140 2.4527193125111484e-305 0.0000000000000000e+00 0.0000000000000000e+00
141 5.9215651973487318e-308 0.0000000000000000e+00 0.0000000000000000e+00
142 1.4194957707119193e-310 0.0000000000000000e+00 0.0000000000000000e+00
143 3.3787997922713783e-313 0.0000000000000000e+00 0.0000000000000000e+00
144 7.9862540736922495e-316 0.0000000000000000e+00 0.0000000000000000e+00
145 1.8745492888556488e-318 0.0000000000000000e+00 0.0000000000000000e+00
146 4.3675403092366195e-321 0.0000000000000000e+00 0.0000000000000000e+00
147 9.8813129168249309e-324 0.0000000000000000e+00 0.0000000000000000e+00
148 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
149 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
150 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
151 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
152 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
153 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
154 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
155 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
156 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
157 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
158 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
159 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
160 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
161 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
162 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
163 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
164 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
165 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
166 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
167 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
168 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
169 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
170 0.0000000000000000e+00 0.0000000000000000e+00 0.0000000000000000e+00
k PBinomial T_Integral Difference
1 1 0.53979461869358936 0.500000000000000000 0.039794618693589356
2 2 0.53979461869358936 0.500000000000000000 0.039794618693589356
3 3 0.53979461869358936 0.500000000000000000 0.039794618693589356
4 4 0.53979461869358936 0.500000000000000000 0.039794618693589356
5 5 0.53979461869358936 0.500000000000000000 0.039794618693589356
6 6 0.53979461869358936 0.500000000000000000 0.039794618693589356
7 7 0.53979461869358936 0.500000000000000000 0.039794618693589356
8 8 0.53979461869358936 0.500000000000000000 0.039794618693589356
9 9 0.53979461869358936 0.500000000000000000 0.039794618693589356
10 10 0.53979461869358936 0.499999999999999889 0.039794618693589467
11 11 0.53979461869358936 0.499999999999999389 0.039794618693589967
12 12 0.53979461869358936 0.499999999999996891 0.039794618693592465
13 13 0.53979461869358936 0.499999999999985179 0.039794618693604178
14 14 0.53979461869358847 0.499999999999931888 0.039794618693656580
15 15 0.53979461869358292 0.499999999999698963 0.039794618693883954
16 16 0.53979461869354806 0.499999999998720190 0.039794618694827866
17 17 0.53979461869334822 0.499999999994769018 0.039794618698579198
18 18 0.53979461869228640 0.499999999979442111 0.039794618712844287
19 19 0.53979461868704037 0.499999999922311533 0.039794618764728840
20 20 0.53979461866285039 0.499999999717684218 0.039794618945166171
21 21 0.53979461855845123 0.499999999013412355 0.039794619545038878
22 22 0.53979461813563501 0.499999996684254044 0.039794621451380963
23 23 0.53979461652490612 0.499999989282409740 0.039794627242496383
24 24 0.53979461074092527 0.499999966679551489 0.039794644061373785
25 25 0.53979459112568562 0.499999900355736826 0.039794690769948793
26 26 0.53979452819345841 0.499999713348428132 0.039794814845030280
27 27 0.53979433687948775 0.499999206671848051 0.039795130207639695
28 28 0.53979378501226472 0.499997887545297504 0.039795897466967212
29 29 0.53979227248728301 0.499994587456092321 0.039797685031190688
30 30 0.53978832911858121 0.499986654250984097 0.039801674867597114
31 31 0.53977853868594150 0.499968328758166880 0.039810209927774620
32 32 0.53975536799536150 0.499927651956074859 0.039827716039286643
33 33 0.53970304708114836 0.499840891409842447 0.039862155671305910
34 34 0.53959023010987606 0.499663070734323145 0.039927159375552912
35 35 0.53935775877513326 0.499312862062084140 0.040044896713049116
36 36 0.53889965349784608 0.498650101968369897 0.040249551529476180
37 37 0.53803579783210442 0.497444869669572076 0.040590928162532347
38 38 0.53647605843562629 0.495338811976281268 0.041137246459345023
39 39 0.53377813083090775 0.491802464075403845 0.041975666755503904
40 40 0.52930525085466362 0.486096552486501410 0.043208698368162213
41 41 0.52219451858473698 0.477249868051820791 0.044944650532916186
42 42 0.51135065187309903 0.464069680887074176 0.047280970986024851
43 43 0.49548157863655568 0.445200708300442005 0.050280870336113670
44 44 0.47318930908998275 0.419243340766228934 0.053945968323753812
45 45 0.44312066644576825 0.384930329778291724 0.058190336667476528
46 46 0.40416810665667202 0.341344746068542926 0.062823360588129096
47 47 0.35569381003024125 0.288144601416603363 0.067549208613637890
48 48 0.29773541188994357 0.225746882249926395 0.071988529640017174
49 49 0.23114491189896336 0.155421741610324182 0.075723170288639174
50 50 0.15761790149225599 0.079259709439103043 0.078358192053152947
ExpRep documentation built on May 2, 2019, 2:12 p.m.
R Package Documentation
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Description Details Author(s) References Examples
Description
The package ExpRep, which basically responds to educational purposes, allows to calculate the probabilities of occurrences of an event in a great number of repetitions of Bernoulli experiment, through the application of the local and the integral theorem of De Moivre Laplace, and the theorem of Poisson. It gives the possibility to show the results graphically and analytically, and to compare the results obtained by the application of the above theorems with those calculated by the direct application of the Binomial formula.
Details
The DESCRIPTION file:
This package was not yet installed at build time.
Index: This package was not yet installed at build time.
Author(s)
Larisa Zamora-Matamoros and Jorge Diaz-Silvera
Maintainer: Larisa Zamora-Matamoros <larisa@uo.edu.cu>
References
Gnedenko, B. V. (1978). The Theory of Probability. Mir Publishers. Moscow.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ProbL<-Local_Theorem(n=100,m=50,p=0.02)
ProbL
ProbI<-Integral_Theorem(n=100,p=0.5,linf=0,lsup=50)
ProbI
ProbP<-Poisson_Theorem(n=100,m=50,p=0.002)
ProbP
beta<-ApplicIntegralTheo(Applic="beta",n=369,p=0.4,alpha=0.05)
beta
alpha<-ApplicIntegralTheo(Applic="alpha",n=369,p=0.4,beta=0.95)
alpha
n<-ApplicIntegralTheo(Applic="n",p=0.4,alpha=0.05,beta=0.95)
n
S_Local_Limit_Theorem(n = 170, p = 0.5, Compare = TRUE, Table = TRUE, Graph = TRUE,
GraphE = TRUE)
S_Poisson_Theorem(n = 169, p = 0.002, Compare = TRUE, Table = TRUE, Graph = TRUE,
GraphE = TRUE)
S_Integral_Theorem(n=100, p=0.5, linf = 0, lsup = 50, Compare = TRUE, Table = TRUE,
Graph = TRUE, GraphE = TRUE)
Buffon(p = 0.5, width = 0.2, r = c(100, 500, 1000, 1500))
|
Example output
[1] 1.570307e-256
[1] 0.5
[1] 3.030861e-100
[1] 0.95006827243625058
[1] 0.049985095799422834
[1] 369
m x PBinomial TLocal
1 0 -13.03840481040529653 6.6819117752305559e-52 7.4419138643607013e-39
2 1 -12.88501181263582218 1.1359250017891868e-49 5.4345583489117509e-38
3 2 -12.73161881486634783 9.5985662651187374e-48 3.8763696021741189e-37
4 3 -12.57822581709687348 5.3751971084665718e-46 2.7006444336879435e-36
5 4 -12.42483281932740091 2.2441447927847241e-44 1.8377690984236611e-35
6 5 -12.27143982155792656 7.4505607120452671e-43 1.2215065128760695e-34
7 6 -12.11804682378845222 2.0489041958124106e-41 7.9301597373135953e-34
8 7 -11.96465382601897787 4.8002898301891583e-40 5.0286266217181697e-33
9 8 -11.81126082824950352 9.7805905290106760e-39 3.1145703961477821e-32
10 9 -11.65786783048002917 1.7605062952218917e-37 1.8842052899791108e-31
11 10 -11.50447483271055660 2.8344151353071975e-36 1.1133701987435749e-30
12 11 -11.35108183494108225 4.1227856513559951e-35 6.4258749910530849e-30
13 12 -11.19768883717160790 5.4626909880467249e-34 3.6224821896093798e-29
14 13 -11.04429583940213355 6.6392705854720298e-33 1.9946263479627000e-28
15 14 -10.89090284163265920 7.4454677279936815e-32 1.0727490794078742e-27
16 15 -10.73750984386318486 7.7432864371137072e-31 5.6352872156522522e-27
17 16 -10.58411684609371051 7.5013087359536756e-30 2.8914472079863166e-26
18 17 -10.43072384832423793 6.7953032078638413e-29 1.4490914207904825e-25
19 18 -10.27733085055476359 5.7760077266841887e-28 7.0934515943270875e-25
20 19 -10.12393785278528924 4.6208061813474098e-27 3.3915696477242618e-24
21 20 -9.97054485501581489 3.4887086669172374e-26 1.5838905832131320e-23
22 21 -9.81715185724634054 2.4919347620838077e-25 7.2248846868644842e-23
23 22 -9.66375885947686619 1.6877194525022136e-24 3.2189777095440539e-22
24 23 -9.51036586170739362 1.0860107781318568e-23 1.4008328742913487e-21
25 24 -9.35697286393791927 6.6518160160576584e-23 5.9543723204776714e-21
26 25 -9.20357986616844492 3.8846605533776366e-22 2.4721052418186992e-20
27 26 -9.05018686839897057 2.1664453086144553e-21 1.0024881094659756e-19
28 27 -8.89679387062949623 1.1554374979277373e-20 3.9707524370429841e-19
29 28 -8.74340087286002188 5.9009843644165918e-20 1.5361997793645551e-18
30 29 -8.59000787509054753 2.8894475163695049e-19 5.8050222942283077e-18
31 30 -8.43661487732107496 1.3580403326936764e-18 2.1426014371814620e-17
32 31 -8.28322187955160061 6.1330853734552610e-18 7.7243189477036549e-17
33 32 -8.12982888178212626 2.6640589590946176e-17 2.7199461796138341e-16
34 33 -7.97643588401265191 1.1140610192577334e-16 9.3549555743936295e-16
35 34 -7.82304288624317756 4.4890105775973291e-16 3.1427110644852564e-15
36 35 -7.66964988847370410 1.7443012530093037e-15 1.0312132532960704e-14
37 36 -7.51625689070422975 6.5411296987848212e-15 3.3050179591336516e-14
38 37 -7.36286389293475541 2.3689496746950673e-14 1.0346190432549043e-13
39 38 -7.20947089516528195 8.2913238614324112e-14 3.1635042202076297e-13
40 39 -7.05607789739580760 2.8062942300233449e-13 9.4479519267978745e-13
41 40 -6.90268489962633325 9.1906136033265523e-13 2.7560572698411681e-12
42 41 -6.74929190185685979 2.9140969961766280e-12 7.8527199052172838e-12
43 42 -6.59589890408738544 8.9504407739712559e-12 2.1854117949406021e-11
44 43 -6.44250590631791109 2.6643172536471990e-11 5.9405651698871143e-11
45 44 -6.28911290854843674 7.6901884366636397e-11 1.5772609560369330e-10
46 45 -6.13571991077896328 2.1532527622657907e-10 4.0903516608474877e-10
47 46 -5.98232691300948893 5.8512303322440968e-10 1.0360937362164591e-09
48 47 -5.82893391524001458 1.5437288536133231e-09 2.5634140201581425e-09
49 48 -5.67554091747054112 3.9558051873841431e-09 6.1946927217086197e-09
50 49 -5.52214791970106678 9.8491476094055301e-09 1.4621842059507159e-08
51 50 -5.36875492193159243 2.3834937214761211e-08 3.3710540397483414e-08
52 51 -5.21536192416211897 5.6082205211203769e-08 7.5912037280779167e-08
53 52 -5.06196892639264462 1.2834196961794589e-07 1.6696939963261641e-07
54 53 -4.90857592862317027 2.8574249839467164e-07 3.5871078186222288e-07
55 54 -4.75518293085369681 6.1910874652178859e-07 7.5271969901508153e-07
56 55 -4.60178993308422246 1.3057566290277394e-06 1.5427780080438974e-06
57 56 -4.44839693531474811 2.6814645060391950e-06 3.0885518982983557e-06
58 57 -4.29500393754527376 5.3629290120784096e-06 6.0393148798809450e-06
59 58 -4.14161093977580030 1.0448465144221465e-05 1.1534579060157566e-05
60 59 -3.98821794200632596 1.9834374511064674e-05 2.1517763650859156e-05
61 60 -3.83482494423685205 3.6693592845468994e-05 3.9207921690589931e-05
62 61 -3.68143194646737770 6.6168773983632875e-05 6.9780136964352985e-05
63 62 -3.52803894869790380 1.1632897361638936e-04 1.2130288201060519e-04
64 63 -3.37464595092842989 1.9942109762809311e-04 2.0596419432700153e-04
65 64 -3.22125295315895555 3.3340714759697167e-04 3.4158094975963397e-04
66 65 -3.06785995538948164 5.4371011761967407e-04 5.5332062959365298e-04
67 66 -2.91446695762000729 8.6499336894037835e-04 8.7547024360817047e-04
68 67 -2.76107395985053339 1.3426762741761313e-03 1.3529670585599644e-03
69 68 -2.60768096208105948 2.0337596505902965e-03 2.0422756642438150e-03
70 69 -2.45428796431158514 3.0064273095682806e-03 3.0110835637272653e-03
71 70 -2.30089496654211123 4.3378451180913795e-03 4.3362325031843551e-03
72 71 -2.14750196877263688 6.1096410113963169e-03 6.0993508950584968e-03
73 72 -1.99410897100316298 8.4007563906699344e-03 8.3798449647355094e-03
74 73 -1.84071597323368885 1.1277727757337718e-02 1.1245263983321315e-02
75 74 -1.68732297546421495 1.4782967465699435e-02 1.4739563839334460e-02
76 75 -1.53392997769474082 1.8922198356095286e-02 1.8870391748974823e-02
77 76 -1.38053697992526669 2.3652747945119110e-02 2.3597093114758723e-02
78 77 -1.22714398215579257 2.8874783205729809e-02 2.8821554614928656e-02
79 78 -1.07375098438631844 3.4427626129908621e-02 3.4384095576540964e-02
80 79 -0.92035798661684443 4.0092931695589792e-02 4.0066288543874909e-02
81 80 -0.76696498884737041 4.5605709803733407e-02 4.5601794132324194e-02
82 81 -0.61357199107789628 5.0673010893037079e-02 5.0695107843085743e-02
83 82 -0.46017899330842221 5.4998755725369511e-02 5.5046724165688482e-02
84 83 -0.30678599553894814 5.8311933781114697e-02 5.8381898481733786e-02
85 84 -0.15339299776947407 6.0394502844725924e-02 6.0479230098047461e-02
86 85 0.00000000000000000 6.1105026407605040e-02 6.1194952327765867e-02
87 86 0.15339299776947407 6.0394502844725924e-02 6.0479230098047461e-02
88 87 0.30678599553894814 5.8311933781114697e-02 5.8381898481733786e-02
89 88 0.46017899330842221 5.4998755725369511e-02 5.5046724165688482e-02
90 89 0.61357199107789628 5.0673010893037100e-02 5.0695107843085743e-02
91 90 0.76696498884737041 4.5605709803733394e-02 4.5601794132324194e-02
92 91 0.92035798661684443 4.0092931695589806e-02 4.0066288543874909e-02
93 92 1.07375098438631844 3.4427626129908621e-02 3.4384095576540964e-02
94 93 1.22714398215579257 2.8874783205729809e-02 2.8821554614928656e-02
95 94 1.38053697992526669 2.3652747945119110e-02 2.3597093114758723e-02
96 95 1.53392997769474082 1.8922198356095279e-02 1.8870391748974823e-02
97 96 1.68732297546421495 1.4782967465699435e-02 1.4739563839334460e-02
98 97 1.84071597323368885 1.1277727757337708e-02 1.1245263983321315e-02
99 98 1.99410897100316298 8.4007563906699344e-03 8.3798449647355094e-03
100 99 2.14750196877263688 6.1096410113963169e-03 6.0993508950584968e-03
101 100 2.30089496654211123 4.3378451180913795e-03 4.3362325031843551e-03
102 101 2.45428796431158514 3.0064273095682806e-03 3.0110835637272653e-03
103 102 2.60768096208105948 2.0337596505902965e-03 2.0422756642438150e-03
104 103 2.76107395985053339 1.3426762741761300e-03 1.3529670585599644e-03
105 104 2.91446695762000729 8.6499336894037835e-04 8.7547024360817047e-04
106 105 3.06785995538948164 5.4371011761967407e-04 5.5332062959365298e-04
107 106 3.22125295315895555 3.3340714759697167e-04 3.4158094975963397e-04
108 107 3.37464595092842989 1.9942109762809311e-04 2.0596419432700153e-04
109 108 3.52803894869790380 1.1632897361638936e-04 1.2130288201060519e-04
110 109 3.68143194646737770 6.6168773983632875e-05 6.9780136964352985e-05
111 110 3.83482494423685205 3.6693592845468994e-05 3.9207921690589931e-05
112 111 3.98821794200632596 1.9834374511064674e-05 2.1517763650859156e-05
113 112 4.14161093977580030 1.0448465144221465e-05 1.1534579060157566e-05
114 113 4.29500393754527376 5.3629290120784096e-06 6.0393148798809450e-06
115 114 4.44839693531474811 2.6814645060391950e-06 3.0885518982983557e-06
116 115 4.60178993308422246 1.3057566290277394e-06 1.5427780080438974e-06
117 116 4.75518293085369681 6.1910874652178859e-07 7.5271969901508153e-07
118 117 4.90857592862317027 2.8574249839467164e-07 3.5871078186222288e-07
119 118 5.06196892639264462 1.2834196961794589e-07 1.6696939963261641e-07
120 119 5.21536192416211897 5.6082205211203769e-08 7.5912037280779167e-08
121 120 5.36875492193159243 2.3834937214761211e-08 3.3710540397483414e-08
122 121 5.52214791970106678 9.8491476094055301e-09 1.4621842059507159e-08
123 122 5.67554091747054112 3.9558051873841431e-09 6.1946927217086197e-09
124 123 5.82893391524001458 1.5437288536133231e-09 2.5634140201581425e-09
125 124 5.98232691300948893 5.8512303322440968e-10 1.0360937362164591e-09
126 125 6.13571991077896328 2.1532527622657907e-10 4.0903516608474877e-10
127 126 6.28911290854843674 7.6901884366636397e-11 1.5772609560369330e-10
128 127 6.44250590631791109 2.6643172536471990e-11 5.9405651698871143e-11
129 128 6.59589890408738544 8.9504407739712559e-12 2.1854117949406021e-11
130 129 6.74929190185685979 2.9140969961766280e-12 7.8527199052172838e-12
131 130 6.90268489962633325 9.1906136033265523e-13 2.7560572698411681e-12
132 131 7.05607789739580760 2.8062942300233449e-13 9.4479519267978745e-13
133 132 7.20947089516528195 8.2913238614324415e-14 3.1635042202076297e-13
134 133 7.36286389293475541 2.3689496746950673e-14 1.0346190432549043e-13
135 134 7.51625689070422975 6.5411296987848212e-15 3.3050179591336516e-14
136 135 7.66964988847370410 1.7443012530093037e-15 1.0312132532960704e-14
137 136 7.82304288624317756 4.4890105775973291e-16 3.1427110644852564e-15
138 137 7.97643588401265191 1.1140610192577334e-16 9.3549555743936295e-16
139 138 8.12982888178212626 2.6640589590945988e-17 2.7199461796138341e-16
140 139 8.28322187955160061 6.1330853734552610e-18 7.7243189477036549e-17
141 140 8.43661487732107496 1.3580403326936764e-18 2.1426014371814620e-17
142 141 8.59000787509054753 2.8894475163695049e-19 5.8050222942283077e-18
143 142 8.74340087286002188 5.9009843644165918e-20 1.5361997793645551e-18
144 143 8.89679387062949623 1.1554374979277373e-20 3.9707524370429841e-19
145 144 9.05018686839897057 2.1664453086144553e-21 1.0024881094659756e-19
146 145 9.20357986616844492 3.8846605533776366e-22 2.4721052418186992e-20
147 146 9.35697286393791927 6.6518160160576584e-23 5.9543723204776714e-21
148 147 9.51036586170739362 1.0860107781318568e-23 1.4008328742913487e-21
149 148 9.66375885947686619 1.6877194525022136e-24 3.2189777095440539e-22
150 149 9.81715185724634054 2.4919347620837903e-25 7.2248846868644842e-23
151 150 9.97054485501581489 3.4887086669172374e-26 1.5838905832131320e-23
152 151 10.12393785278528924 4.6208061813474098e-27 3.3915696477242618e-24
153 152 10.27733085055476359 5.7760077266841887e-28 7.0934515943270875e-25
154 153 10.43072384832423793 6.7953032078638413e-29 1.4490914207904825e-25
155 154 10.58411684609371051 7.5013087359536756e-30 2.8914472079863166e-26
156 155 10.73750984386318486 7.7432864371137072e-31 5.6352872156522522e-27
157 156 10.89090284163265920 7.4454677279937877e-32 1.0727490794078742e-27
158 157 11.04429583940213355 6.6392705854720298e-33 1.9946263479627000e-28
159 158 11.19768883717160790 5.4626909880467249e-34 3.6224821896093798e-29
160 159 11.35108183494108225 4.1227856513559951e-35 6.4258749910530849e-30
161 160 11.50447483271055660 2.8344151353071975e-36 1.1133701987435749e-30
162 161 11.65786783048002917 1.7605062952218917e-37 1.8842052899791108e-31
163 162 11.81126082824950352 9.7805905290106760e-39 3.1145703961477821e-32
164 163 11.96465382601897787 4.8002898301891583e-40 5.0286266217181697e-33
165 164 12.11804682378845222 2.0489041958124106e-41 7.9301597373135953e-34
166 165 12.27143982155792656 7.4505607120452671e-43 1.2215065128760695e-34
167 166 12.42483281932740091 2.2441447927847241e-44 1.8377690984236611e-35
168 167 12.57822581709687348 5.3751971084665718e-46 2.7006444336879435e-36
169 168 12.73161881486634783 9.5985662651187374e-48 3.8763696021741189e-37
170 169 12.88501181263582218 1.1359250017892029e-49 5.4345583489117509e-38
171 170 13.03840481040529653 6.6819117752305559e-52 7.4419138643607013e-39
Difference
1 7.4419138643600331e-39
2 5.4345583489003916e-38
3 3.8763696020781333e-37
4 2.7006444331504238e-36
5 1.8377690961795164e-35
6 1.2215065054255088e-34
7 7.9301595324231765e-34
8 5.0286261416891864e-33
9 3.1145694180887292e-32
10 1.8842035294728156e-31
11 1.1133673643284396e-30
12 6.4258337631965715e-30
13 3.6224275626994994e-29
14 1.9945599552568454e-28
15 1.0726746247305942e-27
16 5.6345128870085410e-27
17 2.8906970771127210e-26
18 1.4484118904696962e-25
19 7.0876755866004035e-25
20 3.3869488415429145e-24
21 1.5804018745462147e-23
22 7.1999653392436462e-23
23 3.2021005150190317e-22
24 1.3899727665100302e-21
25 5.8878541603170950e-21
26 2.4332586362849229e-20
27 9.8082365637983105e-20
28 3.8552086872502105e-19
29 1.4771899357203892e-18
30 5.5160775425913572e-18
31 2.0067974039120942e-17
32 7.1110104103581292e-17
33 2.4535402837043726e-16
34 8.2408945551358961e-16
35 2.6938100067255235e-15
36 8.5678312799514006e-15
37 2.6509049892551695e-14
38 7.9772407578539758e-14
39 2.3343718340643886e-13
40 6.6416576967745300e-13
41 1.8369959095085126e-12
42 4.9386229090406554e-12
43 1.2903677175434765e-11
44 3.2762479162399156e-11
45 8.0824211237056903e-11
46 1.9370988985816970e-10
47 4.5097070299204944e-10
48 1.0196851665448194e-09
49 2.2388875343244765e-09
50 4.7726944501016292e-09
51 9.8756031827222032e-09
52 1.9829832069575398e-08
53 3.8627430014670522e-08
54 7.2968283467551244e-08
55 1.3361095249329293e-07
56 2.3702137901615796e-07
57 4.0708739225916063e-07
58 6.7638586780253542e-07
59 1.0861139159361013e-06
60 1.6833891397944817e-06
61 2.5143288451209370e-06
62 3.6113629807201100e-06
63 4.9739083942158271e-06
64 6.5430966989084240e-06
65 8.1738021626622946e-06
66 9.6105119739789023e-06
67 1.0476874667792119e-05
68 1.0290784383833098e-05
69 8.5160136535184991e-06
70 4.6562541589846747e-06
71 1.6126149070243984e-06
72 1.0290116337820059e-05
73 2.0911425934425076e-05
74 3.2463774016402991e-05
75 4.3403626364974662e-05
76 5.1806607120463005e-05
77 5.5654830360386820e-05
78 5.3228590801153441e-05
79 4.3530553367657210e-05
80 2.6643151714883517e-05
81 3.9156714092131173e-06
82 2.2096950048663966e-05
83 4.7968440318971184e-05
84 6.9964700619089271e-05
85 8.4727253321537077e-05
86 8.9925920160827122e-05
87 8.4727253321537077e-05
88 6.9964700619089271e-05
89 4.7968440318971184e-05
90 2.2096950048643149e-05
91 3.9156714091992395e-06
92 2.6643151714897395e-05
93 4.3530553367657210e-05
94 5.3228590801153441e-05
95 5.5654830360386820e-05
96 5.1806607120456066e-05
97 4.3403626364974662e-05
98 3.2463774016392583e-05
99 2.0911425934425076e-05
100 1.0290116337820059e-05
101 1.6126149070243984e-06
102 4.6562541589846747e-06
103 8.5160136535184991e-06
104 1.0290784383834399e-05
105 1.0476874667792119e-05
106 9.6105119739789023e-06
107 8.1738021626622946e-06
108 6.5430966989084240e-06
109 4.9739083942158271e-06
110 3.6113629807201100e-06
111 2.5143288451209370e-06
112 1.6833891397944817e-06
113 1.0861139159361013e-06
114 6.7638586780253542e-07
115 4.0708739225916063e-07
116 2.3702137901615796e-07
117 1.3361095249329293e-07
118 7.2968283467551244e-08
119 3.8627430014670522e-08
120 1.9829832069575398e-08
121 9.8756031827222032e-09
122 4.7726944501016292e-09
123 2.2388875343244765e-09
124 1.0196851665448194e-09
125 4.5097070299204944e-10
126 1.9370988985816970e-10
127 8.0824211237056903e-11
128 3.2762479162399156e-11
129 1.2903677175434765e-11
130 4.9386229090406554e-12
131 1.8369959095085126e-12
132 6.6416576967745300e-13
133 2.3343718340643855e-13
134 7.9772407578539758e-14
135 2.6509049892551695e-14
136 8.5678312799514006e-15
137 2.6938100067255235e-15
138 8.2408945551358961e-16
139 2.4535402837043740e-16
140 7.1110104103581292e-17
141 2.0067974039120942e-17
142 5.5160775425913572e-18
143 1.4771899357203892e-18
144 3.8552086872502105e-19
145 9.8082365637983105e-20
146 2.4332586362849229e-20
147 5.8878541603170950e-21
148 1.3899727665100302e-21
149 3.2021005150190317e-22
150 7.1999653392436462e-23
151 1.5804018745462147e-23
152 3.3869488415429145e-24
153 7.0876755866004035e-25
154 1.4484118904696962e-25
155 2.8906970771127210e-26
156 5.6345128870085410e-27
157 1.0726746247305942e-27
158 1.9945599552568454e-28
159 3.6224275626994994e-29
160 6.4258337631965715e-30
161 1.1133673643284396e-30
162 1.8842035294728156e-31
163 3.1145694180887292e-32
164 5.0286261416891864e-33
165 7.9301595324231765e-34
166 1.2215065054255088e-34
167 1.8377690961795164e-35
168 2.7006444331504238e-36
169 3.8763696020781333e-37
170 5.4345583489003916e-38
171 7.4419138643600331e-39
m x PBinomial TPoisson
1 0 -0.58195992534659879 7.1295394683814373e-01 7.1319528789828224e-01
2 1 1.13981500171434424 2.4146135674478209e-01 2.4106000730961941e-01
3 2 2.86158992877528728 4.0646801536195799e-02 4.0739141235325689e-02
4 3 4.58336485583623077 4.5344127298227776e-03 4.5899432458466945e-03
5 4 6.30513978289717336 3.7711047753035131e-04 3.8785020427404605e-04
6 5 8.02691470995811684 2.4939169856716626e-05 2.6218673808925528e-05
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105 104 178.48263248899149858 8.9497682155296332e-234 7.0428676913198811e-216
106 105 180.20440741605244739 1.1102871152007615e-236 2.2671326473011088e-218
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Difference1 TLocal Difference2
1 2.4134106013851131e-04 5.7988729257321758e-01 1.3306665426492614e-01
2 4.0134943516267896e-04 3.5873477236220347e-01 1.1727341561742138e-01
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6 1.2795039522089013e-06 7.0112336811908773e-15 2.4939169849705392e-05
7 1.1091185887089757e-07 1.5844372441809378e-21 1.3660734323652339e-06
8 7.5698035256042140e-09 1.8470803417829573e-29 6.3747486251226370e-08
9 4.2620840572171813e-10 1.1107764750536744e-38 2.5869470873493718e-09
10 2.0420029104678042e-11 3.4458605959779781e-49 9.2740699412880757e-11
11 8.5118294332015719e-13 5.5144077750200545e-61 2.9736496805733343e-12
12 3.1388890654028626e-14 4.5522928776651959e-74 8.6137784516516593e-14
13 1.0374940103548386e-15 1.9386153892610541e-88 2.2728406736155061e-15
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15 8.4959823500700957e-19 4.8261965822649502e-121 1.2283461366166612e-18
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18 1.0817178488059485e-23 1.3235827884358059e-179 8.8491756187102855e-24
19 2.1953817883678901e-25 1.0621685357493945e-201 1.4975224827922158e-25
20 4.1844396717728959e-27 4.3970954886414686e-225 2.3850426632383229e-27
21 7.5176916843878684e-29 9.3900629788878500e-250 3.5847334617810187e-29
22 1.2772515928979485e-30 1.0344303557034564e-275 5.0971016872351015e-31
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k PBinomial T_Integral Difference
1 1 0.53979461869358936 0.500000000000000000 0.039794618693589356
2 2 0.53979461869358936 0.500000000000000000 0.039794618693589356
3 3 0.53979461869358936 0.500000000000000000 0.039794618693589356
4 4 0.53979461869358936 0.500000000000000000 0.039794618693589356
5 5 0.53979461869358936 0.500000000000000000 0.039794618693589356
6 6 0.53979461869358936 0.500000000000000000 0.039794618693589356
7 7 0.53979461869358936 0.500000000000000000 0.039794618693589356
8 8 0.53979461869358936 0.500000000000000000 0.039794618693589356
9 9 0.53979461869358936 0.500000000000000000 0.039794618693589356
10 10 0.53979461869358936 0.499999999999999889 0.039794618693589467
11 11 0.53979461869358936 0.499999999999999389 0.039794618693589967
12 12 0.53979461869358936 0.499999999999996891 0.039794618693592465
13 13 0.53979461869358936 0.499999999999985179 0.039794618693604178
14 14 0.53979461869358847 0.499999999999931888 0.039794618693656580
15 15 0.53979461869358292 0.499999999999698963 0.039794618693883954
16 16 0.53979461869354806 0.499999999998720190 0.039794618694827866
17 17 0.53979461869334822 0.499999999994769018 0.039794618698579198
18 18 0.53979461869228640 0.499999999979442111 0.039794618712844287
19 19 0.53979461868704037 0.499999999922311533 0.039794618764728840
20 20 0.53979461866285039 0.499999999717684218 0.039794618945166171
21 21 0.53979461855845123 0.499999999013412355 0.039794619545038878
22 22 0.53979461813563501 0.499999996684254044 0.039794621451380963
23 23 0.53979461652490612 0.499999989282409740 0.039794627242496383
24 24 0.53979461074092527 0.499999966679551489 0.039794644061373785
25 25 0.53979459112568562 0.499999900355736826 0.039794690769948793
26 26 0.53979452819345841 0.499999713348428132 0.039794814845030280
27 27 0.53979433687948775 0.499999206671848051 0.039795130207639695
28 28 0.53979378501226472 0.499997887545297504 0.039795897466967212
29 29 0.53979227248728301 0.499994587456092321 0.039797685031190688
30 30 0.53978832911858121 0.499986654250984097 0.039801674867597114
31 31 0.53977853868594150 0.499968328758166880 0.039810209927774620
32 32 0.53975536799536150 0.499927651956074859 0.039827716039286643
33 33 0.53970304708114836 0.499840891409842447 0.039862155671305910
34 34 0.53959023010987606 0.499663070734323145 0.039927159375552912
35 35 0.53935775877513326 0.499312862062084140 0.040044896713049116
36 36 0.53889965349784608 0.498650101968369897 0.040249551529476180
37 37 0.53803579783210442 0.497444869669572076 0.040590928162532347
38 38 0.53647605843562629 0.495338811976281268 0.041137246459345023
39 39 0.53377813083090775 0.491802464075403845 0.041975666755503904
40 40 0.52930525085466362 0.486096552486501410 0.043208698368162213
41 41 0.52219451858473698 0.477249868051820791 0.044944650532916186
42 42 0.51135065187309903 0.464069680887074176 0.047280970986024851
43 43 0.49548157863655568 0.445200708300442005 0.050280870336113670
44 44 0.47318930908998275 0.419243340766228934 0.053945968323753812
45 45 0.44312066644576825 0.384930329778291724 0.058190336667476528
46 46 0.40416810665667202 0.341344746068542926 0.062823360588129096
47 47 0.35569381003024125 0.288144601416603363 0.067549208613637890
48 48 0.29773541188994357 0.225746882249926395 0.071988529640017174
49 49 0.23114491189896336 0.155421741610324182 0.075723170288639174
50 50 0.15761790149225599 0.079259709439103043 0.078358192053152947
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