nhpp.plot: Plot simulated non-homogeneous Poisson processes
In poisson: Simulating Homogenous & Non-Homogenous Poisson Processes
Description
Usage
Arguments
Value
Author(s)
See Also
Examples
Description
Plot num.events simulated non-homogeneous Poisson processes, plus
the mean and quantiles
Usage
1
2
Arguments
rate
the rate at which events occur in the Poisson process, aka lambda
num.events
the number of event times to simulate in each process
prob.func
function that takes time as sole argument and returns value
between 0 and 1
num.sims
number of simulated paths to plot
t0
start time
t1
end time
num.points
number of points to use in estimating mean and quantile processes
quantiles
plot these quantile processes
...
further arguments to be passed to or from methods
Value
list
x
Matrix of event times, one process per column
x.bar
Vector of mean process event times
x.q
Matrix of quantile event times, one process per column
Author(s)
Kristian Brock - Author, Daniel Slade - Contributor
See Also
Examples
1
2
3
Example output
$x
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.0000000
[2,] 0.2045989 1.619056 0.5679248 1.686961 0.7934367 2.080071 0.7200466
[3,] 1.4417378 1.761045 1.1337059 2.556705 1.3820858 2.118511 1.1031255
[4,] 1.5317001 2.257629 1.1989125 3.284914 1.3967570 2.283131 1.5140122
[5,] 1.5864765 2.496379 1.4373078 4.068713 1.5282271 2.740421 2.3888025
[6,] 1.7556185 2.758339 1.6958336 4.215448 2.1266414 2.774409 2.5304315
[7,] 1.8610342 2.871385 1.8547473 4.231794 2.2840017 2.827432 2.5353097
[8,] 1.9262279 2.944408 2.0405909 4.767286 2.2850671 3.048385 2.9161884
[9,] 2.1269222 3.024137 2.3399073 4.992065 2.4537951 3.153121 3.1685317
[10,] 2.3684458 3.106672 2.6692981 5.167625 2.6739194 3.239029 3.1734276
[11,] 2.3950419 3.259135 2.8132524 5.665643 2.6938564 3.277174 3.2359127
[12,] 2.4512583 3.389246 2.9998808 5.827823 2.7742674 3.278302 3.4569382
[13,] 2.6355131 3.486201 3.0095122 5.992931 3.6452579 3.347193 3.5028012
[14,] 2.9206958 4.038488 3.1129111 6.046508 4.0014464 4.671260 3.6974262
[15,] 2.9905220 4.317748 3.1269366 6.093230 4.6363009 4.703047 4.1210940
[16,] 3.1176535 4.397038 3.2395374 6.197467 4.6872271 4.741706 4.6198838
[17,] 3.5412967 4.595570 3.5082971 6.371767 4.7226967 5.195922 4.7299781
[18,] 3.8539344 4.605027 3.6286164 6.519104 4.9331763 5.198312 4.9302387
[19,] 3.8957192 4.980935 3.6712640 6.552949 4.9719014 5.482646 5.4295274
[20,] 3.9136629 5.588237 3.6965394 6.562371 5.7544075 6.188761 5.4701359
[21,] 3.9891490 5.807126 3.7911607 7.048464 6.6321869 6.414221 5.5425988
[,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15]
[1,] 0.000000 0.000000 0.0000000 0.000000 0.000000 0.000000 0.0000000 0.000000
[2,] 1.187990 1.012811 0.6102471 1.960964 1.011926 1.596325 0.1894076 1.485921
[3,] 1.394227 1.306696 1.1982450 2.116109 1.658248 2.106641 0.4623407 1.804227
[4,] 1.659842 1.559805 1.5503112 2.219741 1.670315 2.180706 1.5219980 2.379089
[5,] 1.707795 1.581362 1.5757372 2.926903 1.938490 2.191291 1.5708393 2.562333
[6,] 1.755367 1.908887 2.4228495 2.935313 2.447141 2.192844 1.7815190 2.604955
[7,] 1.779965 1.963112 2.8205508 2.998918 2.897166 2.458110 2.0097781 3.234169
[8,] 2.288000 2.920755 3.1426319 3.011941 3.114414 2.479706 2.1086230 3.424294
[9,] 2.832548 2.936899 3.3988458 3.114477 3.123770 2.835899 2.2840246 3.474967
[10,] 3.105753 3.536223 3.4700469 3.244139 3.292562 2.875348 2.4208584 3.829819
[11,] 3.611624 3.564937 3.7586430 3.284832 3.324207 2.966590 2.5425326 4.036285
[12,] 3.639287 3.703721 4.1481883 4.058812 4.095981 2.994715 2.5566529 4.227623
[13,] 3.732345 4.376008 4.1967160 4.087576 4.242358 3.399006 2.6419139 4.495388
[14,] 3.961380 4.592888 4.3383371 4.502103 4.333793 3.641350 3.0774145 4.949152
[15,] 4.042556 4.680784 4.4116117 4.628533 4.695451 3.750833 3.1882720 5.081872
[16,] 4.518531 4.770031 4.5349889 4.841339 4.727577 3.899810 4.1016155 5.223452
[17,] 4.686976 4.886479 4.5401149 5.141128 4.749993 4.667078 5.1601536 5.318805
[18,] 4.764478 4.974550 5.2754385 5.352329 4.838022 4.884393 5.2244489 5.453132
[19,] 4.814691 5.264686 5.3179555 5.447576 4.851846 5.330381 5.4768515 5.571708
[20,] 5.320427 5.538474 5.6440474 5.812067 4.912892 5.343810 5.8358708 5.651572
[21,] 5.421630 5.667614 5.9370074 5.933909 5.070536 5.400216 5.8846997 6.139246
[,16] [,17] [,18] [,19] [,20] [,21] [,22]
[1,] 0.000000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.0000000
[2,] 1.486211 0.8421448 0.2250178 0.800902 1.284113 0.9329371 0.7697194
[3,] 1.645347 1.8046862 1.5211647 1.195863 1.333306 1.2731078 1.1090142
[4,] 1.879380 2.0899630 1.5678469 2.215042 1.643218 1.3435715 1.9145366
[5,] 1.905133 2.4655127 1.8042039 2.221510 2.101018 1.5883324 1.9186417
[6,] 2.136251 2.6174687 2.0342725 2.282994 2.435530 2.1021929 2.2205190
[7,] 2.427446 2.7749212 2.1138972 2.359664 2.494163 2.4250264 2.4740331
[8,] 3.228380 2.8681138 2.4657699 2.606261 2.696142 2.4400409 2.5615302
[9,] 3.255747 3.1482315 2.7126381 2.818865 2.725199 2.5194995 2.5702758
[10,] 3.665157 3.1951496 3.3480447 3.646048 4.094450 2.6752225 2.6452669
[11,] 3.697567 3.5946058 3.5313741 3.863689 4.148504 2.8326278 2.7268805
[12,] 3.797017 3.6386407 3.5766480 4.012718 4.168506 3.4430254 2.8512293
[13,] 3.934754 3.6704964 3.6680525 4.069329 4.231501 3.5226038 3.0255383
[14,] 4.065303 3.6904626 4.3155243 4.476076 4.525276 3.6832555 3.1543955
[15,] 4.096074 4.0676073 4.9520066 5.438163 4.864168 3.7692587 3.4529836
[16,] 4.225491 4.1632765 5.1409600 5.586119 5.274820 4.0653909 3.9892587
[17,] 4.243210 4.4013101 5.1489178 5.760013 5.324094 4.4293742 4.0821969
[18,] 5.107182 4.8771950 5.2029281 5.766802 5.677083 4.6073445 4.1114408
[19,] 5.353197 5.2540711 5.2836058 6.367152 5.698072 4.7291407 4.4285401
[20,] 5.470930 5.3701130 5.4344204 6.475690 5.739161 4.8330953 4.5277931
[21,] 5.495864 5.9493220 6.1083017 6.600884 5.851089 5.1999133 4.6573420
[,23] [,24] [,25] [,26] [,27] [,28] [,29]
[1,] 0.0000000 0.0000000 0.000000 0.000000 0.000000 0.000000 0.0000000
[2,] 0.5643064 0.9631471 1.137967 1.146441 1.118421 1.226225 0.7650914
[3,] 2.3787778 1.0419039 1.182402 1.592240 1.387897 1.506955 1.4931208
[4,] 2.5494876 1.3575490 1.540897 3.010043 2.413306 1.604152 2.1284419
[5,] 2.6383782 1.5996882 2.415880 3.236943 2.479224 2.111722 2.5853029
[6,] 2.9644359 2.2862571 2.703896 3.424340 2.509706 2.539260 2.6217639
[7,] 3.0387506 2.7502915 4.004637 3.712777 3.042210 2.668807 2.7106798
[8,] 3.1852889 3.1436447 4.233647 3.720189 3.172347 2.737645 2.7351622
[9,] 3.3421588 3.2053248 4.351944 3.827020 3.365180 2.922043 2.8837132
[10,] 3.8899885 3.5819575 4.393748 3.854124 3.440995 3.150757 3.4980725
[11,] 3.9422845 3.8864682 4.483743 4.010975 3.608481 3.255089 3.5569154
[12,] 4.3196416 3.9638352 4.759513 4.029337 3.735616 3.370967 4.1164190
[13,] 4.9130794 4.1533051 5.143354 4.107667 3.990131 4.158879 4.3717480
[14,] 5.0479524 4.4353677 5.966895 4.520294 4.413774 4.383915 4.5707584
[15,] 5.2252899 4.4636350 6.136272 4.561381 4.439110 4.396664 4.6450746
[16,] 5.3004661 4.5968102 6.216888 5.204147 4.445140 4.441157 4.7283512
[17,] 5.6154876 4.5985920 6.448612 5.297913 4.445705 4.754166 4.8177288
[18,] 5.7795886 4.7621165 7.294508 5.346644 4.616698 4.854540 4.9444487
[19,] 5.8996708 4.8544950 7.489312 6.032284 4.986348 4.857439 4.9875004
[20,] 6.1528858 5.5371225 8.490071 6.296515 5.936260 4.875262 5.4169383
[21,] 6.2702580 5.5932907 8.592889 6.412158 6.228558 5.317260 5.4471444
[,30] [,31] [,32] [,33] [,34] [,35] [,36]
[1,] 0.000000 0.000000 0.000000 0.000000 0.0000000 0.000000 0.0000000
[2,] 1.383648 1.230811 1.093483 1.219506 0.4937438 1.148246 0.4626796
[3,] 2.185233 1.353322 1.574221 1.500479 0.6490960 2.175595 1.1559494
[4,] 2.308373 1.661715 1.594628 1.955911 1.4141618 2.223013 2.0783614
[5,] 2.494606 1.897179 1.967747 2.706811 2.4287926 2.387626 2.1579188
[6,] 2.667563 2.036662 2.439020 3.132657 3.4784115 2.536917 2.5053414
[7,] 2.688330 2.630074 2.729854 3.428738 3.5840537 2.658774 2.5890863
[8,] 2.709356 2.907355 2.828358 3.570511 3.6599319 2.722010 2.7063902
[9,] 2.795637 3.201973 3.045990 3.589324 3.9405840 2.935391 2.7334831
[10,] 2.874341 3.498121 3.275448 3.716683 4.2223353 3.108572 3.1325257
[11,] 3.249889 3.507590 3.302309 3.731346 4.6438476 3.370742 3.8343268
[12,] 3.583370 3.937238 3.315555 4.056167 4.8060362 4.117684 3.9384284
[13,] 3.907583 4.111477 3.590832 4.108778 5.1676838 4.131923 3.9486994
[14,] 3.918734 4.133851 3.883013 4.226027 5.2202577 5.036277 4.0124749
[15,] 4.013438 4.297221 4.041679 4.379805 5.2680058 5.113099 4.0497896
[16,] 4.035458 4.467687 4.285682 4.606240 5.3055302 5.226291 4.2327427
[17,] 4.071338 4.514448 4.289678 4.837685 5.4701173 5.953437 4.3226062
[18,] 4.091822 4.546485 4.400707 4.901472 5.4735686 6.115333 4.4138419
[19,] 4.095969 4.631885 4.601419 5.137552 5.4960957 6.439908 4.4364982
[20,] 4.184188 4.649404 4.725050 5.207197 5.7256632 6.535740 4.4443951
[21,] 4.366275 4.727836 4.966853 5.481287 5.8827528 6.709813 4.4616298
[,37] [,38] [,39] [,40] [,41] [,42] [,43]
[1,] 0.0000000 0.000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
[2,] 0.8404597 1.129867 0.8790928 0.3601199 1.251054 0.3337812 1.394751
[3,] 1.4455674 1.444018 1.1681594 1.5902127 2.027294 1.0682050 2.011022
[4,] 1.6556791 1.888744 1.3523311 1.6855662 2.643510 1.3446151 2.356553
[5,] 1.7283647 2.029424 1.3891879 1.7527350 2.700821 1.6753993 2.455899
[6,] 2.7328494 2.083256 1.5037590 1.7880418 2.880577 1.8454611 2.534727
[7,] 2.9126376 2.217737 1.7883061 2.3367425 2.929711 2.2271154 3.089342
[8,] 2.9251991 2.928333 1.9289636 2.5531657 3.057617 2.3874575 3.106161
[9,] 3.0033650 3.378174 2.2408547 2.8017599 3.087601 2.5372506 3.186573
[10,] 3.0443704 3.754969 2.5550449 2.9753522 3.217669 2.7913673 3.359046
[11,] 3.1400570 3.879953 2.7507291 2.9842581 3.641445 2.8404660 3.582514
[12,] 3.3397693 4.188037 2.8817548 3.1197950 3.756188 2.8436279 4.167967
[13,] 3.4373725 4.530615 3.1194189 3.3694362 3.762424 2.8797756 4.171869
[14,] 4.1262492 4.604518 3.1766147 3.4338797 4.314133 3.2807669 4.212715
[15,] 4.1323219 4.689351 3.2109917 3.6640483 4.537384 3.3339226 4.330734
[16,] 4.1611162 4.825845 3.2716421 3.7719465 4.733655 3.4259841 4.350271
[17,] 4.7337410 5.119833 3.4199336 4.0354211 4.984164 3.5152895 4.352936
[18,] 4.8062711 5.436271 3.6447779 4.1810187 4.991430 3.6430778 4.460851
[19,] 4.9948629 5.439034 3.7382776 4.2970887 5.180730 4.0587828 5.237186
[20,] 5.2376176 5.470901 3.9055680 4.3052734 5.237860 4.4258577 5.317519
[21,] 5.7632608 5.607509 4.0312597 4.5898107 5.259405 4.7766825 5.489968
[,44] [,45] [,46] [,47] [,48] [,49] [,50] [,51]
[1,] 0.000000 0.000000 0.000000 0.000000 0.0000000 0.000000 0.0000000 0.000000
[2,] 1.380987 1.454006 1.203494 1.076076 0.5302546 1.266321 0.7357999 1.012614
[3,] 1.447921 1.670366 2.200746 1.267060 0.8732506 1.461274 1.2594911 2.032201
[4,] 1.493148 1.724542 2.235504 1.438685 1.1610606 2.120242 1.5784445 3.399116
[5,] 1.524219 1.908643 2.267339 1.557087 1.6697118 2.133888 1.6270422 3.409462
[6,] 1.537435 2.174675 2.562170 1.817371 1.7669143 2.317354 2.0373137 3.413314
[7,] 1.875911 2.602121 2.886540 2.021148 1.9309088 2.834122 2.1671000 3.420460
[8,] 2.001984 2.959932 3.015738 2.175898 2.1197324 2.893417 2.2557623 3.756409
[9,] 2.028830 3.031421 3.077612 2.255133 2.5935018 3.058431 2.3904260 4.642435
[10,] 2.241394 3.191350 3.165505 2.342494 2.7935783 3.105226 2.4456097 4.659118
[11,] 2.874041 3.585828 3.292063 2.429853 3.0363801 3.188431 2.4807865 5.112142
[12,] 3.128975 3.608198 3.515607 2.582123 3.1976778 3.410450 2.5825468 5.125650
[13,] 3.276595 3.655251 4.696394 3.275675 3.4463636 3.422223 2.5861715 5.524899
[14,] 3.429477 4.056954 4.705322 3.436513 3.5501831 3.523651 3.0093893 5.534807
[15,] 3.430699 4.063419 4.827255 4.339925 3.8584331 3.816758 3.5231282 5.945590
[16,] 3.440646 4.350667 5.391501 4.584761 3.9256210 3.921971 3.6757830 6.417013
[17,] 3.580047 4.432446 5.538922 4.609148 3.9279222 4.150865 3.7110011 6.872306
[18,] 4.022297 4.674628 5.694896 4.693763 3.9597095 4.159528 4.1791388 6.925620
[19,] 4.204366 4.904304 5.834702 5.024829 3.9967543 4.692470 4.3447986 7.313251
[20,] 4.556712 4.964954 5.862757 5.079723 4.1352824 4.826662 4.4926156 7.752760
[21,] 5.805035 4.971098 6.091279 5.174646 4.2089220 4.907745 4.5885131 7.900976
[,52] [,53] [,54] [,55] [,56] [,57] [,58]
[1,] 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.0000000 0.0000000
[2,] 0.3727345 0.7102533 0.976544 1.517374 0.7286131 0.7048591 0.8298504
[3,] 2.3612859 1.1669451 1.091748 1.675728 1.8432226 2.0384793 1.6406144
[4,] 2.4024121 1.5975664 1.328661 1.689822 2.0640582 2.2166278 2.3453603
[5,] 2.4374741 1.9227489 1.329671 2.193437 2.1318959 2.3474088 2.3475629
[6,] 2.8361671 2.0059157 1.730909 2.212143 2.2273246 2.9687617 2.3697216
[7,] 3.0360353 2.0126733 2.366445 2.244988 2.4258451 3.2701500 2.7353919
[8,] 3.0370304 2.3955991 2.480660 2.511480 2.6442146 3.3325473 2.8413469
[9,] 3.5178577 2.6428397 2.489476 2.626819 2.7800366 4.1803367 3.2140478
[10,] 3.6591508 2.6640647 3.005499 2.787641 3.4065011 4.2115782 3.3072348
[11,] 3.9852949 2.7507207 3.023556 2.868695 3.5214163 4.2182857 3.3654053
[12,] 4.1240646 2.9666398 3.087410 2.894377 3.5504948 4.2239494 3.8003053
[13,] 4.4239722 3.0080850 3.158227 3.456368 3.6951223 4.3191319 4.0449513
[14,] 4.4660315 3.4230203 3.233309 3.600920 3.9824923 4.4816205 4.0986153
[15,] 4.6244790 3.4241367 3.254286 3.664523 4.1202334 4.6072954 4.2165641
[16,] 4.8279513 3.7912584 3.262032 4.030336 4.1629069 4.8024364 4.2848767
[17,] 4.8505462 3.8394473 3.468655 4.432685 4.1782264 4.8566151 4.3538370
[18,] 4.9224048 3.9436196 3.570629 4.663270 4.4062930 5.1727245 4.4665778
[19,] 5.1743590 3.9803687 3.779115 4.831366 4.4510969 5.1989071 4.5855808
[20,] 5.2561522 4.6845480 3.850046 5.800947 4.6284264 5.3545560 4.5885453
[21,] 5.3564952 4.7884130 3.917981 5.949038 5.1657370 5.4926064 4.8963868
[,59] [,60] [,61] [,62] [,63] [,64] [,65]
[1,] 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.0000000
[2,] 0.8086639 0.5589404 0.8648158 0.9537601 0.201749 0.1984554 0.7796095
[3,] 1.3561767 1.5661470 0.9269426 1.0033026 1.879404 0.5248047 1.5295415
[4,] 1.4021963 2.0731644 1.5818125 1.0179999 2.395429 1.7401318 1.8733501
[5,] 1.6627530 2.1724754 1.6996090 1.3966548 2.800819 1.7764529 2.2611879
[6,] 1.8718782 2.2748026 1.7873940 3.1500874 3.285038 2.7287966 2.9098666
[7,] 1.9300872 2.6706805 2.0011588 3.2106069 3.327154 2.7706777 3.0794243
[8,] 2.0962619 2.7001628 2.0400550 3.2148640 3.759796 2.8776438 3.1317192
[9,] 2.2199101 2.8901016 2.2330138 3.5157201 3.833379 3.0903008 3.1714248
[10,] 2.8310028 2.9560454 2.2360493 3.6486577 4.169155 3.1684325 3.9835437
[11,] 3.0177899 3.6829767 2.2692726 3.8203141 4.234451 3.2281532 4.2327512
[12,] 3.1938895 3.9346219 2.3379264 4.0038085 4.574782 3.3779730 4.7861637
[13,] 3.3320070 3.9478959 3.2561071 4.5622995 4.940458 3.4607770 4.9379512
[14,] 3.8412072 4.1504265 3.3491180 4.8457194 5.245584 3.7215265 5.2428356
[15,] 4.3425898 4.1858131 3.3963562 4.9358279 5.331277 3.7372302 5.2707042
[16,] 4.5365528 4.4431358 3.8090698 5.4926324 5.413674 3.9617004 5.6713478
[17,] 4.5464639 4.9441129 4.1365603 5.5135513 5.510398 4.4143105 5.7138845
[18,] 4.6986188 5.0601621 4.4149986 5.7556119 5.747211 4.4478994 5.8753854
[19,] 4.7325186 5.0884355 4.4878462 5.7813822 5.763930 4.5142259 6.1957179
[20,] 5.0232530 5.2270004 4.5113215 5.7876863 6.189957 4.9234298 6.2743199
[21,] 5.0327902 5.2684731 4.9522499 5.8772044 6.567079 5.0887850 6.4398144
[,66] [,67] [,68] [,69] [,70] [,71] [,72]
[1,] 0.0000000 0.000000 0.000000 0.000000 0.000000 0.0000000 0.0000000
[2,] 0.8951798 1.446639 1.052189 1.179013 2.277009 0.8749356 0.3968867
[3,] 1.0529812 1.736604 1.203816 1.279156 2.690644 1.8786013 1.2698745
[4,] 1.1471144 1.910915 1.385968 1.761738 2.834583 2.3005066 1.3623864
[5,] 1.3675962 2.008790 2.270298 1.942266 2.892622 2.8866273 1.3694865
[6,] 1.5867125 2.055939 2.443339 1.982248 2.949545 3.3787778 1.4340875
[7,] 1.7099500 2.176228 3.050044 2.046395 2.981309 3.3788329 1.4475822
[8,] 1.8664566 2.529233 3.124330 2.458315 3.238064 3.4307322 1.5012756
[9,] 2.5185804 2.557792 3.319533 2.476789 3.250308 3.5203456 2.3397254
[10,] 2.6113238 2.748437 3.331863 2.562001 3.387208 3.6057327 2.4521532
[11,] 2.9156924 2.833004 3.581774 2.582118 3.474327 4.1672197 2.5174270
[12,] 3.0098780 3.348701 3.743959 2.591438 3.845311 5.2194820 2.5581787
[13,] 3.6220068 3.377379 3.941528 2.631778 3.931154 5.5490196 2.7467176
[14,] 4.0207366 3.866174 3.967999 2.753080 3.936809 5.8117755 2.8282302
[15,] 4.1163924 4.004351 4.052486 3.956177 4.079015 5.8862713 3.1540323
[16,] 4.3429000 4.038236 4.334655 4.063530 4.122543 6.1151003 3.8359229
[17,] 4.7354509 4.073978 4.536072 4.596199 4.477599 6.1433636 4.0468964
[18,] 4.8729176 4.355526 4.659098 4.769061 4.686791 6.2179536 4.6116682
[19,] 4.9506179 4.387216 4.764746 4.868215 4.865352 6.2391563 5.6977315
[20,] 4.9930875 4.488013 5.472837 5.602980 5.280760 6.3215186 5.9149068
[21,] 5.0092580 4.583030 5.889018 5.774853 5.438529 6.4945730 6.3475546
[,73] [,74] [,75] [,76] [,77] [,78] [,79]
[1,] 0.000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 0.000000
[2,] 1.501966 0.4479679 0.4069625 0.1218515 1.190680 0.9737199 1.524574
[3,] 1.510246 1.0610411 0.5953488 0.8960209 1.999967 1.1833354 1.613796
[4,] 1.612628 1.2137034 1.2504865 1.1121251 2.022251 1.3033666 2.238948
[5,] 2.531401 1.2746442 2.1051076 2.1533156 2.072261 1.3184419 2.431552
[6,] 2.951392 1.8567642 2.5149812 2.5273285 2.141942 1.6058587 2.445724
[7,] 2.992684 2.2848992 2.6877338 2.7360914 2.270514 2.7945579 2.840721
[8,] 3.181243 2.2932987 2.7911870 2.8295009 2.486874 2.9825800 3.336030
[9,] 3.449520 2.3307193 3.0759195 3.3500437 2.902057 3.2062277 3.382846
[10,] 3.617519 2.5439113 3.1780936 3.3583945 3.014276 3.4289381 3.497141
[11,] 3.669952 2.5485839 3.2970056 3.8876220 3.251687 3.4869837 3.640710
[12,] 3.760345 2.7675967 3.3244032 4.1890588 3.275801 3.5207837 3.672363
[13,] 3.907938 2.8077957 3.4888460 4.9830597 3.397098 3.7537588 3.716019
[14,] 4.261171 3.1273998 3.7257448 5.0301568 3.627868 3.9278221 3.745483
[15,] 4.714079 3.2270405 3.7711961 5.1093520 3.647404 4.1515650 4.469448
[16,] 4.861806 3.2828969 4.8182125 5.1909103 3.705456 4.1844798 4.617328
[17,] 4.995212 3.4076898 4.8771712 5.2191116 3.818990 4.2957388 4.917234
[18,] 5.380995 3.8021372 4.9344731 5.2839953 3.820270 4.3315528 5.013737
[19,] 5.524771 4.0388906 5.2959698 5.3830934 4.004688 4.8419488 5.911790
[20,] 5.843558 4.1142911 5.3111047 5.5420194 4.227860 5.0970127 6.179004
[21,] 5.982660 4.1420856 5.3243952 5.5986887 4.701710 5.3118203 6.201462
[,80] [,81] [,82] [,83] [,84] [,85] [,86]
[1,] 0.000000 0.0000000 0.00000000 0.0000000 0.000000 0.0000000 0.000000
[2,] 1.058016 0.4419884 0.06107098 0.9476345 1.572354 0.5536658 2.194968
[3,] 1.487405 0.5968860 0.68087616 2.2507416 1.768391 1.1014824 2.431219
[4,] 1.658864 0.7535172 0.97227251 2.3881351 2.227330 1.5177497 2.639690
[5,] 1.659157 0.7585714 1.63459138 2.5245906 2.519458 1.7595100 3.107090
[6,] 2.249195 0.9360099 1.89172123 2.8626729 2.861247 1.9755107 3.316493
[7,] 2.956078 1.3786909 2.22453507 3.7314011 3.519654 2.1215605 3.536813
[8,] 3.475561 1.5729450 2.22877571 3.8087706 3.776683 2.3310197 3.685439
[9,] 3.834428 1.6680969 2.60632954 3.8858523 4.049798 2.6175731 3.945676
[10,] 3.902584 1.8091196 2.68656626 4.2316163 4.471479 3.1804293 4.060004
[11,] 4.096019 1.9820003 2.79629617 4.4908745 4.539978 3.3610998 4.208607
[12,] 4.185749 2.5267624 2.86589759 4.8355654 4.562582 3.4555459 4.223815
[13,] 4.225665 2.9232789 2.95947841 5.2732771 4.582403 3.5161630 4.281769
[14,] 4.555357 3.0512082 3.29271166 5.4035170 4.710548 3.6369802 4.519602
[15,] 4.837211 3.1959693 3.73971563 5.6128203 4.913405 3.7947292 4.719754
[16,] 4.839630 3.3445176 3.92364945 5.8475664 5.972856 3.8002674 4.857338
[17,] 4.853706 3.3587878 4.36637841 5.8479528 6.063287 4.1372978 5.063603
[18,] 4.856295 3.6434251 4.56805404 5.9834131 6.676572 4.3784207 5.253848
[19,] 5.303718 3.8123681 4.85485797 6.0727703 6.687630 4.8021639 5.873701
[20,] 5.712115 4.0806904 4.99731744 6.2606507 7.158648 5.0663966 5.921498
[21,] 5.754382 4.2649396 5.14444731 6.4631495 7.402085 5.2077345 6.009184
[,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94]
[1,] 0.0000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
[2,] 0.5071650 1.496897 1.176197 1.402018 1.545622 1.498300 1.022916 1.908868
[3,] 0.6956551 1.848362 1.499842 2.170649 1.573662 2.058198 2.150041 2.007364
[4,] 0.9097210 2.226784 1.637305 2.361475 1.929061 2.138138 2.339202 2.361571
[5,] 0.9856138 2.351299 1.668101 2.913541 2.366410 2.242551 3.166717 2.486940
[6,] 1.0288698 2.500737 1.749133 2.919578 2.372562 2.494219 3.465535 2.699427
[7,] 1.1440458 2.611903 1.931821 2.965209 2.692976 2.574138 3.501982 2.743027
[8,] 1.6044934 2.741661 1.932741 3.011492 3.568223 2.703064 3.660400 2.834395
[9,] 1.9874693 3.080505 2.026649 3.197161 3.571358 2.931635 3.669789 2.843449
[10,] 2.0644712 3.117567 2.097370 3.225581 3.639298 3.139288 3.728454 2.858312
[11,] 2.5511122 3.306784 2.191354 3.343779 4.369994 3.306934 3.731641 2.961107
[12,] 2.8480239 3.422245 2.328200 3.634871 4.774873 3.767032 4.009755 2.961927
[13,] 3.0529025 3.760245 2.369192 3.967132 4.947103 3.774057 4.551502 3.103722
[14,] 3.3313809 3.877929 2.433173 3.973854 5.756843 4.018856 4.743242 3.219400
[15,] 3.6359218 3.988828 2.776580 4.170373 5.805818 4.076158 5.182639 3.438813
[16,] 3.6519608 4.075288 3.245903 4.566009 5.861724 4.109679 5.344153 3.592259
[17,] 3.6752189 4.241651 3.283243 5.789512 6.176365 4.210509 5.491897 3.757802
[18,] 3.7089946 4.264049 3.543978 5.885035 6.347230 4.356290 6.188383 4.364699
[19,] 4.7795902 4.430400 3.930082 6.164817 6.397165 4.419399 6.426984 4.425967
[20,] 4.8298820 4.542258 3.960180 6.387644 6.794028 4.657082 6.766363 4.583500
[21,] 5.1290438 4.919888 4.050965 6.599259 6.832131 4.754263 7.056251 4.634014
[,95] [,96] [,97] [,98] [,99] [,100]
[1,] 0.0000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
[2,] 0.2125489 0.2935358 1.693463 0.8603076 1.410956 1.627498
[3,] 0.7375728 0.9622950 1.755300 0.9790316 1.658713 2.793081
[4,] 2.4283434 1.4986284 1.926137 0.9912686 2.025515 2.797082
[5,] 2.6613040 1.6128459 2.183217 1.2940309 2.349464 2.816064
[6,] 2.8710460 1.8206678 2.593652 1.5517619 2.701568 2.988243
[7,] 2.9639378 1.9105961 2.638568 2.6138896 2.760467 3.118818
[8,] 3.2811184 1.9475461 2.797806 3.4837528 3.251173 3.208736
[9,] 3.4193536 2.3162632 3.100559 3.5170703 3.618144 3.219491
[10,] 3.5304197 2.3595959 3.249537 3.5680926 3.732945 4.098530
[11,] 3.8423474 2.7382475 3.313109 3.6368480 3.803169 5.268192
[12,] 3.9736057 2.8753661 3.463179 3.7127762 4.544981 5.663054
[13,] 4.0551375 2.9565040 4.114652 3.8542242 4.841718 5.880354
[14,] 4.1304325 3.4432224 4.383450 4.1519636 4.862218 6.001219
[15,] 4.3494433 3.6469957 4.550125 4.4318023 5.062560 6.318180
[16,] 4.4718443 3.7144690 4.773557 4.4565055 5.158808 6.338124
[17,] 4.6822775 3.8355661 4.787307 4.7335067 5.167717 6.352593
[18,] 5.1870980 3.9216052 4.794044 4.8222676 5.446306 6.740388
[19,] 5.9005345 4.2487450 4.945331 4.8855908 5.805161 6.987033
[20,] 6.4390936 4.3220391 5.149792 5.1143700 5.817155 7.088326
[21,] 6.8325641 4.7033341 5.445238 5.6041960 5.835917 8.190517
$x.bar
[1] 0.000000000 0.007596475 0.030385901 0.068368276 0.121543602
[6] 0.189911879 0.273473105 0.372227282 0.486174409 0.615314487
[11] 0.759647515 0.919173493 1.093892421 1.283804300 1.488909129
[16] 1.709206908 1.944697638 2.195381318 2.461257948 2.742327528
[21] 3.038590059 3.350045540 3.676693972 4.018535353 4.375569685
[26] 4.747796968 5.135217200 5.537830383 5.955636516 6.388635600
[31] 6.836827633 7.300212617 7.776253113 8.253626118 8.731019507
[36] 9.208396648 9.685774916 10.163159220 10.640538187 11.117926374
[41] 11.595306107 12.072649745 12.550076364 13.027450980 13.504839314
[46] 13.982220669 14.459602447 14.936980568 15.414368850 15.891695401
[51] 16.369132238 16.846522843 17.323897926 17.801283837 18.278658587
[56] 18.756060436 19.233428259 19.710807147 20.000000000 20.000000000
[61] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[66] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[71] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[76] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[81] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[86] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[91] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[96] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
$x.q
2.5% 97.5%
[1,] 0.0000000 0.000000
[2,] 0.1937053 2.023495
[3,] 0.5960790 2.497099
[4,] 0.9812957 2.926700
[5,] 1.2838529 3.203586
[6,] 1.4671814 3.445967
[7,] 1.5722069 3.722555
[8,] 1.7289259 3.793529
[9,] 2.0276850 4.270430
[10,] 2.1632425 4.434557
[11,] 2.3290130 4.889702
[12,] 2.4871227 5.174912
[13,] 2.6335523 5.537562
[14,] 2.8721514 5.893213
[15,] 3.1398071 6.023101
[16,] 3.2535641 6.207663
[17,] 3.4135056 6.362660
[18,] 3.6354856 6.710076
[19,] 3.7949101 6.844817
[20,] 3.9094131 7.125245
[21,] 4.0091516 7.664003
poisson documentation built on May 2, 2019, 6:53 a.m.
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Description Usage Arguments Value Author(s) See Also Examples
Description
Plot num.events simulated non-homogeneous Poisson processes, plus the mean and quantiles
Usage
1 2 |
Arguments
rate |
the rate at which events occur in the Poisson process, aka lambda |
num.events |
the number of event times to simulate in each process |
prob.func |
function that takes time as sole argument and returns value between 0 and 1 |
num.sims |
number of simulated paths to plot |
t0 |
start time |
t1 |
end time |
num.points |
number of points to use in estimating mean and quantile processes |
quantiles |
plot these quantile processes |
... |
further arguments to be passed to or from methods |
Value
list
x |
Matrix of event times, one process per column |
x.bar |
Vector of mean process event times |
x.q |
Matrix of quantile event times, one process per column |
Author(s)
Kristian Brock - Author, Daniel Slade - Contributor
See Also
Examples
1 2 3 |
Example output
$x
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.0000000 0.000000 0.0000000 0.000000 0.0000000 0.000000 0.0000000
[2,] 0.2045989 1.619056 0.5679248 1.686961 0.7934367 2.080071 0.7200466
[3,] 1.4417378 1.761045 1.1337059 2.556705 1.3820858 2.118511 1.1031255
[4,] 1.5317001 2.257629 1.1989125 3.284914 1.3967570 2.283131 1.5140122
[5,] 1.5864765 2.496379 1.4373078 4.068713 1.5282271 2.740421 2.3888025
[6,] 1.7556185 2.758339 1.6958336 4.215448 2.1266414 2.774409 2.5304315
[7,] 1.8610342 2.871385 1.8547473 4.231794 2.2840017 2.827432 2.5353097
[8,] 1.9262279 2.944408 2.0405909 4.767286 2.2850671 3.048385 2.9161884
[9,] 2.1269222 3.024137 2.3399073 4.992065 2.4537951 3.153121 3.1685317
[10,] 2.3684458 3.106672 2.6692981 5.167625 2.6739194 3.239029 3.1734276
[11,] 2.3950419 3.259135 2.8132524 5.665643 2.6938564 3.277174 3.2359127
[12,] 2.4512583 3.389246 2.9998808 5.827823 2.7742674 3.278302 3.4569382
[13,] 2.6355131 3.486201 3.0095122 5.992931 3.6452579 3.347193 3.5028012
[14,] 2.9206958 4.038488 3.1129111 6.046508 4.0014464 4.671260 3.6974262
[15,] 2.9905220 4.317748 3.1269366 6.093230 4.6363009 4.703047 4.1210940
[16,] 3.1176535 4.397038 3.2395374 6.197467 4.6872271 4.741706 4.6198838
[17,] 3.5412967 4.595570 3.5082971 6.371767 4.7226967 5.195922 4.7299781
[18,] 3.8539344 4.605027 3.6286164 6.519104 4.9331763 5.198312 4.9302387
[19,] 3.8957192 4.980935 3.6712640 6.552949 4.9719014 5.482646 5.4295274
[20,] 3.9136629 5.588237 3.6965394 6.562371 5.7544075 6.188761 5.4701359
[21,] 3.9891490 5.807126 3.7911607 7.048464 6.6321869 6.414221 5.5425988
[,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15]
[1,] 0.000000 0.000000 0.0000000 0.000000 0.000000 0.000000 0.0000000 0.000000
[2,] 1.187990 1.012811 0.6102471 1.960964 1.011926 1.596325 0.1894076 1.485921
[3,] 1.394227 1.306696 1.1982450 2.116109 1.658248 2.106641 0.4623407 1.804227
[4,] 1.659842 1.559805 1.5503112 2.219741 1.670315 2.180706 1.5219980 2.379089
[5,] 1.707795 1.581362 1.5757372 2.926903 1.938490 2.191291 1.5708393 2.562333
[6,] 1.755367 1.908887 2.4228495 2.935313 2.447141 2.192844 1.7815190 2.604955
[7,] 1.779965 1.963112 2.8205508 2.998918 2.897166 2.458110 2.0097781 3.234169
[8,] 2.288000 2.920755 3.1426319 3.011941 3.114414 2.479706 2.1086230 3.424294
[9,] 2.832548 2.936899 3.3988458 3.114477 3.123770 2.835899 2.2840246 3.474967
[10,] 3.105753 3.536223 3.4700469 3.244139 3.292562 2.875348 2.4208584 3.829819
[11,] 3.611624 3.564937 3.7586430 3.284832 3.324207 2.966590 2.5425326 4.036285
[12,] 3.639287 3.703721 4.1481883 4.058812 4.095981 2.994715 2.5566529 4.227623
[13,] 3.732345 4.376008 4.1967160 4.087576 4.242358 3.399006 2.6419139 4.495388
[14,] 3.961380 4.592888 4.3383371 4.502103 4.333793 3.641350 3.0774145 4.949152
[15,] 4.042556 4.680784 4.4116117 4.628533 4.695451 3.750833 3.1882720 5.081872
[16,] 4.518531 4.770031 4.5349889 4.841339 4.727577 3.899810 4.1016155 5.223452
[17,] 4.686976 4.886479 4.5401149 5.141128 4.749993 4.667078 5.1601536 5.318805
[18,] 4.764478 4.974550 5.2754385 5.352329 4.838022 4.884393 5.2244489 5.453132
[19,] 4.814691 5.264686 5.3179555 5.447576 4.851846 5.330381 5.4768515 5.571708
[20,] 5.320427 5.538474 5.6440474 5.812067 4.912892 5.343810 5.8358708 5.651572
[21,] 5.421630 5.667614 5.9370074 5.933909 5.070536 5.400216 5.8846997 6.139246
[,16] [,17] [,18] [,19] [,20] [,21] [,22]
[1,] 0.000000 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.0000000
[2,] 1.486211 0.8421448 0.2250178 0.800902 1.284113 0.9329371 0.7697194
[3,] 1.645347 1.8046862 1.5211647 1.195863 1.333306 1.2731078 1.1090142
[4,] 1.879380 2.0899630 1.5678469 2.215042 1.643218 1.3435715 1.9145366
[5,] 1.905133 2.4655127 1.8042039 2.221510 2.101018 1.5883324 1.9186417
[6,] 2.136251 2.6174687 2.0342725 2.282994 2.435530 2.1021929 2.2205190
[7,] 2.427446 2.7749212 2.1138972 2.359664 2.494163 2.4250264 2.4740331
[8,] 3.228380 2.8681138 2.4657699 2.606261 2.696142 2.4400409 2.5615302
[9,] 3.255747 3.1482315 2.7126381 2.818865 2.725199 2.5194995 2.5702758
[10,] 3.665157 3.1951496 3.3480447 3.646048 4.094450 2.6752225 2.6452669
[11,] 3.697567 3.5946058 3.5313741 3.863689 4.148504 2.8326278 2.7268805
[12,] 3.797017 3.6386407 3.5766480 4.012718 4.168506 3.4430254 2.8512293
[13,] 3.934754 3.6704964 3.6680525 4.069329 4.231501 3.5226038 3.0255383
[14,] 4.065303 3.6904626 4.3155243 4.476076 4.525276 3.6832555 3.1543955
[15,] 4.096074 4.0676073 4.9520066 5.438163 4.864168 3.7692587 3.4529836
[16,] 4.225491 4.1632765 5.1409600 5.586119 5.274820 4.0653909 3.9892587
[17,] 4.243210 4.4013101 5.1489178 5.760013 5.324094 4.4293742 4.0821969
[18,] 5.107182 4.8771950 5.2029281 5.766802 5.677083 4.6073445 4.1114408
[19,] 5.353197 5.2540711 5.2836058 6.367152 5.698072 4.7291407 4.4285401
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[6,] 1.0288698 2.500737 1.749133 2.919578 2.372562 2.494219 3.465535 2.699427
[7,] 1.1440458 2.611903 1.931821 2.965209 2.692976 2.574138 3.501982 2.743027
[8,] 1.6044934 2.741661 1.932741 3.011492 3.568223 2.703064 3.660400 2.834395
[9,] 1.9874693 3.080505 2.026649 3.197161 3.571358 2.931635 3.669789 2.843449
[10,] 2.0644712 3.117567 2.097370 3.225581 3.639298 3.139288 3.728454 2.858312
[11,] 2.5511122 3.306784 2.191354 3.343779 4.369994 3.306934 3.731641 2.961107
[12,] 2.8480239 3.422245 2.328200 3.634871 4.774873 3.767032 4.009755 2.961927
[13,] 3.0529025 3.760245 2.369192 3.967132 4.947103 3.774057 4.551502 3.103722
[14,] 3.3313809 3.877929 2.433173 3.973854 5.756843 4.018856 4.743242 3.219400
[15,] 3.6359218 3.988828 2.776580 4.170373 5.805818 4.076158 5.182639 3.438813
[16,] 3.6519608 4.075288 3.245903 4.566009 5.861724 4.109679 5.344153 3.592259
[17,] 3.6752189 4.241651 3.283243 5.789512 6.176365 4.210509 5.491897 3.757802
[18,] 3.7089946 4.264049 3.543978 5.885035 6.347230 4.356290 6.188383 4.364699
[19,] 4.7795902 4.430400 3.930082 6.164817 6.397165 4.419399 6.426984 4.425967
[20,] 4.8298820 4.542258 3.960180 6.387644 6.794028 4.657082 6.766363 4.583500
[21,] 5.1290438 4.919888 4.050965 6.599259 6.832131 4.754263 7.056251 4.634014
[,95] [,96] [,97] [,98] [,99] [,100]
[1,] 0.0000000 0.0000000 0.000000 0.0000000 0.000000 0.000000
[2,] 0.2125489 0.2935358 1.693463 0.8603076 1.410956 1.627498
[3,] 0.7375728 0.9622950 1.755300 0.9790316 1.658713 2.793081
[4,] 2.4283434 1.4986284 1.926137 0.9912686 2.025515 2.797082
[5,] 2.6613040 1.6128459 2.183217 1.2940309 2.349464 2.816064
[6,] 2.8710460 1.8206678 2.593652 1.5517619 2.701568 2.988243
[7,] 2.9639378 1.9105961 2.638568 2.6138896 2.760467 3.118818
[8,] 3.2811184 1.9475461 2.797806 3.4837528 3.251173 3.208736
[9,] 3.4193536 2.3162632 3.100559 3.5170703 3.618144 3.219491
[10,] 3.5304197 2.3595959 3.249537 3.5680926 3.732945 4.098530
[11,] 3.8423474 2.7382475 3.313109 3.6368480 3.803169 5.268192
[12,] 3.9736057 2.8753661 3.463179 3.7127762 4.544981 5.663054
[13,] 4.0551375 2.9565040 4.114652 3.8542242 4.841718 5.880354
[14,] 4.1304325 3.4432224 4.383450 4.1519636 4.862218 6.001219
[15,] 4.3494433 3.6469957 4.550125 4.4318023 5.062560 6.318180
[16,] 4.4718443 3.7144690 4.773557 4.4565055 5.158808 6.338124
[17,] 4.6822775 3.8355661 4.787307 4.7335067 5.167717 6.352593
[18,] 5.1870980 3.9216052 4.794044 4.8222676 5.446306 6.740388
[19,] 5.9005345 4.2487450 4.945331 4.8855908 5.805161 6.987033
[20,] 6.4390936 4.3220391 5.149792 5.1143700 5.817155 7.088326
[21,] 6.8325641 4.7033341 5.445238 5.6041960 5.835917 8.190517
$x.bar
[1] 0.000000000 0.007596475 0.030385901 0.068368276 0.121543602
[6] 0.189911879 0.273473105 0.372227282 0.486174409 0.615314487
[11] 0.759647515 0.919173493 1.093892421 1.283804300 1.488909129
[16] 1.709206908 1.944697638 2.195381318 2.461257948 2.742327528
[21] 3.038590059 3.350045540 3.676693972 4.018535353 4.375569685
[26] 4.747796968 5.135217200 5.537830383 5.955636516 6.388635600
[31] 6.836827633 7.300212617 7.776253113 8.253626118 8.731019507
[36] 9.208396648 9.685774916 10.163159220 10.640538187 11.117926374
[41] 11.595306107 12.072649745 12.550076364 13.027450980 13.504839314
[46] 13.982220669 14.459602447 14.936980568 15.414368850 15.891695401
[51] 16.369132238 16.846522843 17.323897926 17.801283837 18.278658587
[56] 18.756060436 19.233428259 19.710807147 20.000000000 20.000000000
[61] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[66] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[71] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[76] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[81] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[86] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[91] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
[96] 20.000000000 20.000000000 20.000000000 20.000000000 20.000000000
$x.q
2.5% 97.5%
[1,] 0.0000000 0.000000
[2,] 0.1937053 2.023495
[3,] 0.5960790 2.497099
[4,] 0.9812957 2.926700
[5,] 1.2838529 3.203586
[6,] 1.4671814 3.445967
[7,] 1.5722069 3.722555
[8,] 1.7289259 3.793529
[9,] 2.0276850 4.270430
[10,] 2.1632425 4.434557
[11,] 2.3290130 4.889702
[12,] 2.4871227 5.174912
[13,] 2.6335523 5.537562
[14,] 2.8721514 5.893213
[15,] 3.1398071 6.023101
[16,] 3.2535641 6.207663
[17,] 3.4135056 6.362660
[18,] 3.6354856 6.710076
[19,] 3.7949101 6.844817
[20,] 3.9094131 7.125245
[21,] 4.0091516 7.664003
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