pnbd.PlotTransactionRateHeterogeneity: Pareto/NBD Plot Transaction Rate Heterogeneity
In BTYD: Implementing BTYD Models with the Log Sum Exp Patch
Description
Usage
Arguments
Details
Value
Examples
Description
Plots and returns the estimated gamma distribution of lambda (customers'
propensities to purchase).
Usage
1
pnbd.PlotTransactionRateHeterogeneity(params, lim = NULL)
Arguments
params
Pareto/NBD parameters - a vector with r, alpha, s, and beta, in
that order. r and alpha are unobserved parameters for the NBD transaction
process. s and beta are unobserved parameters for the Pareto (exponential
gamma) dropout process.
lim
The upper-bound of the x-axis. A number is chosen by the function
if none is provided.
Details
This returns the distribution of each customer's Poisson parameter, which
determines the level of their purchasing (using the Pareto/NBD assumption
that purchasing on the individual level can be modeled with a Poisson
distribution).
Value
Distribution of customers' propensities to purchase.
Examples
1
2
3
4
params <- c(0.55, 10.56, 0.61, 11.64)
pnbd.PlotTransactionRateHeterogeneity(params)
params <- c(3, 10.56, 0.61, 11.64)
pnbd.PlotTransactionRateHeterogeneity(params)
Example output
Loading required package: hypergeo
[,1] [,2] [,3] [,4] [,5]
x.axis.ticks 0 0.003314326 0.006628652 0.009942977 0.0132573
heterogeneity Inf 28.520856984 20.160396932 16.220267705 13.7605436
[,6] [,7] [,8] [,9] [,10]
x.axis.ticks 0.01657163 0.01988595 0.02320028 0.02651461 0.02982893
heterogeneity 12.01783098 10.69041431 9.63093578 8.75733809 8.01961441
[,11] [,12] [,13] [,14] [,15] [,16]
x.axis.ticks 0.03314326 0.03645758 0.03977191 0.04308624 0.04640056 0.04971489
heterogeneity 7.38520614 6.83181220 6.34353109 5.90864817 5.51829647 5.16560964
[,17] [,18] [,19] [,20] [,21] [,22]
x.axis.ticks 0.05302921 0.05634354 0.05965786 0.06297219 0.06628652 0.06960084
heterogeneity 4.84516604 4.55261209 4.28440030 4.03760243 3.80977372 3.59885213
[,23] [,24] [,25] [,26] [,27] [,28]
x.axis.ticks 0.07291517 0.07622949 0.07954382 0.08285814 0.08617247 0.0894868
heterogeneity 3.40308255 3.22095880 3.05117870 2.89260881 2.74425654 2.6052477
[,29] [,30] [,31] [,32] [,33] [,34]
x.axis.ticks 0.09280112 0.09611545 0.09942977 0.1027441 0.1060584 0.1093728
heterogeneity 2.47480857 2.35225084 2.23695976 2.1283840 2.0260271 1.9294409
[,35] [,36] [,37] [,38] [,39] [,40]
x.axis.ticks 0.1126871 0.1160014 0.1193157 0.1226301 0.1259444 0.1292587
heterogeneity 1.8382190 1.7519921 1.6704237 1.5932062 1.5200580 1.4507204
[,41] [,42] [,43] [,44] [,45] [,46]
x.axis.ticks 0.132573 0.1358874 0.1392017 0.142516 0.1458303 0.1491447
heterogeneity 1.384955 1.3225438 1.2632829 1.206985 1.1534775 1.1025980
[,47] [,48] [,49] [,50] [,51] [,52]
x.axis.ticks 0.152459 0.1557733 0.1590876 0.1624020 0.1657163 0.1690306
heterogeneity 1.054197 1.0081352 0.9642825 0.9225175 0.8827269 0.8448046
[,53] [,54] [,55] [,56] [,57] [,58]
x.axis.ticks 0.1723449 0.1756593 0.1789736 0.1822879 0.1856022 0.1889166
heterogeneity 0.8086514 0.7741743 0.7412858 0.7099041 0.6799520 0.6513572
[,59] [,60] [,61] [,62] [,63] [,64]
x.axis.ticks 0.1922309 0.1955452 0.1988595 0.2021739 0.2054882 0.2088025
heterogeneity 0.6240513 0.5979701 0.5730531 0.5492429 0.5264858 0.5047306
[,65] [,66] [,67] [,68] [,69] [,70]
x.axis.ticks 0.2121169 0.2154312 0.2187455 0.2220598 0.2253742 0.2286885
heterogeneity 0.4839293 0.4640363 0.4450084 0.4268048 0.4093869 0.3927181
[,71] [,72] [,73] [,74] [,75] [,76]
x.axis.ticks 0.2320028 0.2353171 0.2386315 0.2419458 0.2452601 0.2485744
heterogeneity 0.3767635 0.3614904 0.3468673 0.3328647 0.3194543 0.3066094
[,77] [,78] [,79] [,80] [,81] [,82]
x.axis.ticks 0.2518888 0.2552031 0.2585174 0.2618317 0.2651461 0.2684604
heterogeneity 0.2943045 0.2825154 0.2712192 0.2603939 0.2500187 0.2400738
[,83] [,84] [,85] [,86] [,87] [,88]
x.axis.ticks 0.2717747 0.2750890 0.2784034 0.2817177 0.2850320 0.2883463
heterogeneity 0.2305403 0.2214001 0.2126363 0.2042323 0.1961728 0.1884427
[,89] [,90] [,91] [,92] [,93] [,94]
x.axis.ticks 0.2916607 0.2949750 0.2982893 0.3016036 0.3049180 0.3082323
heterogeneity 0.1810280 0.1739152 0.1670913 0.1605441 0.1542619 0.1482333
[,95] [,96] [,97] [,98] [,99] [,100]
x.axis.ticks 0.3115466 0.3148609 0.3181753 0.3214896 0.3248039 0.3281183
heterogeneity 0.1424477 0.1368950 0.1315652 0.1264491 0.1215378 0.1168227
[,1] [,2] [,3] [,4] [,5] [,6]
x.axis.ticks 0 0.008040583 0.01608117 0.02412175 0.03216233 0.04020291
heterogeneity 0 0.034967252 0.12848315 0.26555432 0.43366616 0.62244394
[,7] [,8] [,9] [,10] [,11] [,12]
x.axis.ticks 0.0482435 0.05628408 0.06432466 0.07236525 0.08040583 0.08844641
heterogeneity 0.8233556 1.02945101 1.23513452 1.43596544 1.62848458 1.81006306
[,13] [,14] [,15] [,16] [,17] [,18]
x.axis.ticks 0.09648699 0.1045276 0.1125682 0.1206087 0.1286493 0.1366899
heterogeneity 1.97877088 2.1332630 2.2726809 2.3965671 2.5047923 2.5974923
[,19] [,20] [,21] [,22] [,23] [,24]
x.axis.ticks 0.1447305 0.1527711 0.1608117 0.1688522 0.1768928 0.1849334
heterogeneity 2.6750144 2.7378711 2.7867017 2.8222388 2.8452813 2.8566709
[,25] [,26] [,27] [,28] [,29] [,30]
x.axis.ticks 0.192974 0.2010146 0.2090552 0.2170957 0.2251363 0.2331769
heterogeneity 2.857273 2.8479602 2.8296015 2.8030497 2.7691343 2.7286550
[,31] [,32] [,33] [,34] [,35] [,36]
x.axis.ticks 0.2412175 0.2492581 0.2572987 0.2653392 0.2733798 0.2814204
heterogeneity 2.6823771 2.6310275 2.5752930 2.5158181 2.4532052 2.3880137
[,37] [,38] [,39] [,40] [,41] [,42]
x.axis.ticks 0.289461 0.2975016 0.3055421 0.3135827 0.3216233 0.3296639
heterogeneity 2.320761 2.2519231 2.1819358 2.1111966 2.0400656 1.9688677
[,43] [,44] [,45] [,46] [,47] [,48]
x.axis.ticks 0.3377045 0.3457451 0.3537856 0.3618262 0.3698668 0.3779074
heterogeneity 1.8978946 1.8274063 1.7576331 1.6887781 1.6210183 1.5545069
[,49] [,50] [,51] [,52] [,53] [,54]
x.axis.ticks 0.385948 0.3939886 0.4020291 0.4100697 0.4181103 0.4261509
heterogeneity 1.489375 1.4257338 1.3636753 1.3032749 1.2445921 1.1876727
[,55] [,56] [,57] [,58] [,59] [,60]
x.axis.ticks 0.4341915 0.4422321 0.4502726 0.4583132 0.4663538 0.4743944
heterogeneity 1.1325496 1.0792443 1.0277681 0.9781230 0.9303030 0.8842950
[,61] [,62] [,63] [,64] [,65] [,66]
x.axis.ticks 0.4824350 0.4904756 0.4985161 0.5065567 0.5145973 0.5226379
heterogeneity 0.8400794 0.7976313 0.7569210 0.7179149 0.6805758 0.6448637
[,67] [,68] [,69] [,70] [,71] [,72]
x.axis.ticks 0.5306785 0.5387190 0.5467596 0.5548002 0.5628408 0.5708814
heterogeneity 0.6107364 0.5781496 0.5470577 0.5174140 0.4891710 0.4622810
[,73] [,74] [,75] [,76] [,77] [,78]
x.axis.ticks 0.5789220 0.5869625 0.5950031 0.6030437 0.6110843 0.6191249
heterogeneity 0.4366958 0.4123675 0.3892484 0.3672913 0.3464495 0.3266772
[,79] [,80] [,81] [,82] [,83] [,84]
x.axis.ticks 0.6271655 0.6352060 0.6432466 0.6512872 0.6593278 0.6673684
heterogeneity 0.3079295 0.2901623 0.2733326 0.2573986 0.2423196 0.2280561
[,85] [,86] [,87] [,88] [,89] [,90]
x.axis.ticks 0.6754090 0.6834495 0.6914901 0.6995307 0.7075713 0.7156119
heterogeneity 0.2145699 0.2018240 0.1897826 0.1784115 0.1676773 0.1575483
[,91] [,92] [,93] [,94] [,95] [,96]
x.axis.ticks 0.7236525 0.7316930 0.7397336 0.7477742 0.7558148 0.7638554
heterogeneity 0.1479937 0.1389843 0.1304918 0.1224893 0.1149510 0.1078522
[,97] [,98] [,99] [,100]
x.axis.ticks 0.7718960 0.77993653 0.78797712 0.79601770
heterogeneity 0.1011693 0.09487997 0.08896269 0.08339708
BTYD documentation built on Nov. 18, 2021, 1:10 a.m.
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Description Usage Arguments Details Value Examples
Description
Plots and returns the estimated gamma distribution of lambda (customers' propensities to purchase).
Usage
1 | pnbd.PlotTransactionRateHeterogeneity(params, lim = NULL)
|
Arguments
params |
Pareto/NBD parameters - a vector with r, alpha, s, and beta, in that order. r and alpha are unobserved parameters for the NBD transaction process. s and beta are unobserved parameters for the Pareto (exponential gamma) dropout process. |
lim |
The upper-bound of the x-axis. A number is chosen by the function if none is provided. |
Details
This returns the distribution of each customer's Poisson parameter, which determines the level of their purchasing (using the Pareto/NBD assumption that purchasing on the individual level can be modeled with a Poisson distribution).
Value
Distribution of customers' propensities to purchase.
Examples
1 2 3 4 | params <- c(0.55, 10.56, 0.61, 11.64)
pnbd.PlotTransactionRateHeterogeneity(params)
params <- c(3, 10.56, 0.61, 11.64)
pnbd.PlotTransactionRateHeterogeneity(params)
|
Example output
Loading required package: hypergeo
[,1] [,2] [,3] [,4] [,5]
x.axis.ticks 0 0.003314326 0.006628652 0.009942977 0.0132573
heterogeneity Inf 28.520856984 20.160396932 16.220267705 13.7605436
[,6] [,7] [,8] [,9] [,10]
x.axis.ticks 0.01657163 0.01988595 0.02320028 0.02651461 0.02982893
heterogeneity 12.01783098 10.69041431 9.63093578 8.75733809 8.01961441
[,11] [,12] [,13] [,14] [,15] [,16]
x.axis.ticks 0.03314326 0.03645758 0.03977191 0.04308624 0.04640056 0.04971489
heterogeneity 7.38520614 6.83181220 6.34353109 5.90864817 5.51829647 5.16560964
[,17] [,18] [,19] [,20] [,21] [,22]
x.axis.ticks 0.05302921 0.05634354 0.05965786 0.06297219 0.06628652 0.06960084
heterogeneity 4.84516604 4.55261209 4.28440030 4.03760243 3.80977372 3.59885213
[,23] [,24] [,25] [,26] [,27] [,28]
x.axis.ticks 0.07291517 0.07622949 0.07954382 0.08285814 0.08617247 0.0894868
heterogeneity 3.40308255 3.22095880 3.05117870 2.89260881 2.74425654 2.6052477
[,29] [,30] [,31] [,32] [,33] [,34]
x.axis.ticks 0.09280112 0.09611545 0.09942977 0.1027441 0.1060584 0.1093728
heterogeneity 2.47480857 2.35225084 2.23695976 2.1283840 2.0260271 1.9294409
[,35] [,36] [,37] [,38] [,39] [,40]
x.axis.ticks 0.1126871 0.1160014 0.1193157 0.1226301 0.1259444 0.1292587
heterogeneity 1.8382190 1.7519921 1.6704237 1.5932062 1.5200580 1.4507204
[,41] [,42] [,43] [,44] [,45] [,46]
x.axis.ticks 0.132573 0.1358874 0.1392017 0.142516 0.1458303 0.1491447
heterogeneity 1.384955 1.3225438 1.2632829 1.206985 1.1534775 1.1025980
[,47] [,48] [,49] [,50] [,51] [,52]
x.axis.ticks 0.152459 0.1557733 0.1590876 0.1624020 0.1657163 0.1690306
heterogeneity 1.054197 1.0081352 0.9642825 0.9225175 0.8827269 0.8448046
[,53] [,54] [,55] [,56] [,57] [,58]
x.axis.ticks 0.1723449 0.1756593 0.1789736 0.1822879 0.1856022 0.1889166
heterogeneity 0.8086514 0.7741743 0.7412858 0.7099041 0.6799520 0.6513572
[,59] [,60] [,61] [,62] [,63] [,64]
x.axis.ticks 0.1922309 0.1955452 0.1988595 0.2021739 0.2054882 0.2088025
heterogeneity 0.6240513 0.5979701 0.5730531 0.5492429 0.5264858 0.5047306
[,65] [,66] [,67] [,68] [,69] [,70]
x.axis.ticks 0.2121169 0.2154312 0.2187455 0.2220598 0.2253742 0.2286885
heterogeneity 0.4839293 0.4640363 0.4450084 0.4268048 0.4093869 0.3927181
[,71] [,72] [,73] [,74] [,75] [,76]
x.axis.ticks 0.2320028 0.2353171 0.2386315 0.2419458 0.2452601 0.2485744
heterogeneity 0.3767635 0.3614904 0.3468673 0.3328647 0.3194543 0.3066094
[,77] [,78] [,79] [,80] [,81] [,82]
x.axis.ticks 0.2518888 0.2552031 0.2585174 0.2618317 0.2651461 0.2684604
heterogeneity 0.2943045 0.2825154 0.2712192 0.2603939 0.2500187 0.2400738
[,83] [,84] [,85] [,86] [,87] [,88]
x.axis.ticks 0.2717747 0.2750890 0.2784034 0.2817177 0.2850320 0.2883463
heterogeneity 0.2305403 0.2214001 0.2126363 0.2042323 0.1961728 0.1884427
[,89] [,90] [,91] [,92] [,93] [,94]
x.axis.ticks 0.2916607 0.2949750 0.2982893 0.3016036 0.3049180 0.3082323
heterogeneity 0.1810280 0.1739152 0.1670913 0.1605441 0.1542619 0.1482333
[,95] [,96] [,97] [,98] [,99] [,100]
x.axis.ticks 0.3115466 0.3148609 0.3181753 0.3214896 0.3248039 0.3281183
heterogeneity 0.1424477 0.1368950 0.1315652 0.1264491 0.1215378 0.1168227
[,1] [,2] [,3] [,4] [,5] [,6]
x.axis.ticks 0 0.008040583 0.01608117 0.02412175 0.03216233 0.04020291
heterogeneity 0 0.034967252 0.12848315 0.26555432 0.43366616 0.62244394
[,7] [,8] [,9] [,10] [,11] [,12]
x.axis.ticks 0.0482435 0.05628408 0.06432466 0.07236525 0.08040583 0.08844641
heterogeneity 0.8233556 1.02945101 1.23513452 1.43596544 1.62848458 1.81006306
[,13] [,14] [,15] [,16] [,17] [,18]
x.axis.ticks 0.09648699 0.1045276 0.1125682 0.1206087 0.1286493 0.1366899
heterogeneity 1.97877088 2.1332630 2.2726809 2.3965671 2.5047923 2.5974923
[,19] [,20] [,21] [,22] [,23] [,24]
x.axis.ticks 0.1447305 0.1527711 0.1608117 0.1688522 0.1768928 0.1849334
heterogeneity 2.6750144 2.7378711 2.7867017 2.8222388 2.8452813 2.8566709
[,25] [,26] [,27] [,28] [,29] [,30]
x.axis.ticks 0.192974 0.2010146 0.2090552 0.2170957 0.2251363 0.2331769
heterogeneity 2.857273 2.8479602 2.8296015 2.8030497 2.7691343 2.7286550
[,31] [,32] [,33] [,34] [,35] [,36]
x.axis.ticks 0.2412175 0.2492581 0.2572987 0.2653392 0.2733798 0.2814204
heterogeneity 2.6823771 2.6310275 2.5752930 2.5158181 2.4532052 2.3880137
[,37] [,38] [,39] [,40] [,41] [,42]
x.axis.ticks 0.289461 0.2975016 0.3055421 0.3135827 0.3216233 0.3296639
heterogeneity 2.320761 2.2519231 2.1819358 2.1111966 2.0400656 1.9688677
[,43] [,44] [,45] [,46] [,47] [,48]
x.axis.ticks 0.3377045 0.3457451 0.3537856 0.3618262 0.3698668 0.3779074
heterogeneity 1.8978946 1.8274063 1.7576331 1.6887781 1.6210183 1.5545069
[,49] [,50] [,51] [,52] [,53] [,54]
x.axis.ticks 0.385948 0.3939886 0.4020291 0.4100697 0.4181103 0.4261509
heterogeneity 1.489375 1.4257338 1.3636753 1.3032749 1.2445921 1.1876727
[,55] [,56] [,57] [,58] [,59] [,60]
x.axis.ticks 0.4341915 0.4422321 0.4502726 0.4583132 0.4663538 0.4743944
heterogeneity 1.1325496 1.0792443 1.0277681 0.9781230 0.9303030 0.8842950
[,61] [,62] [,63] [,64] [,65] [,66]
x.axis.ticks 0.4824350 0.4904756 0.4985161 0.5065567 0.5145973 0.5226379
heterogeneity 0.8400794 0.7976313 0.7569210 0.7179149 0.6805758 0.6448637
[,67] [,68] [,69] [,70] [,71] [,72]
x.axis.ticks 0.5306785 0.5387190 0.5467596 0.5548002 0.5628408 0.5708814
heterogeneity 0.6107364 0.5781496 0.5470577 0.5174140 0.4891710 0.4622810
[,73] [,74] [,75] [,76] [,77] [,78]
x.axis.ticks 0.5789220 0.5869625 0.5950031 0.6030437 0.6110843 0.6191249
heterogeneity 0.4366958 0.4123675 0.3892484 0.3672913 0.3464495 0.3266772
[,79] [,80] [,81] [,82] [,83] [,84]
x.axis.ticks 0.6271655 0.6352060 0.6432466 0.6512872 0.6593278 0.6673684
heterogeneity 0.3079295 0.2901623 0.2733326 0.2573986 0.2423196 0.2280561
[,85] [,86] [,87] [,88] [,89] [,90]
x.axis.ticks 0.6754090 0.6834495 0.6914901 0.6995307 0.7075713 0.7156119
heterogeneity 0.2145699 0.2018240 0.1897826 0.1784115 0.1676773 0.1575483
[,91] [,92] [,93] [,94] [,95] [,96]
x.axis.ticks 0.7236525 0.7316930 0.7397336 0.7477742 0.7558148 0.7638554
heterogeneity 0.1479937 0.1389843 0.1304918 0.1224893 0.1149510 0.1078522
[,97] [,98] [,99] [,100]
x.axis.ticks 0.7718960 0.77993653 0.78797712 0.79601770
heterogeneity 0.1011693 0.09487997 0.08896269 0.08339708
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