# bgnbd.PlotDropoutRateHeterogeneity: BG/NBD Plot Dropout Probability Heterogeneity In BTYD: Implementing BTYD Models with the Log Sum Exp Patch

## Description

Plots and returns the estimated gamma distribution of p (customers' probability of dropping out immediately after a transaction).

## Usage

 `1` ```bgnbd.PlotDropoutRateHeterogeneity(params, lim = NULL) ```

## Arguments

 `params` BG/NBD parameters - a vector with r, alpha, a, and b, in that order. r and alpha are unobserved parameters for the NBD transaction process. a and b are unobserved parameters for the Beta geometric dropout process. `lim` upper-bound of the x-axis. A number is chosen by the function if none is provided.

## Value

Distribution of customers' probabilities of dropping out.

## Examples

 ```1 2 3 4``` ```params <- c(0.243, 4.414, 0.793, 2.426) bgnbd.PlotDropoutRateHeterogeneity(params) params <- c(0.243, 4.414, 1.33, 2.426) bgnbd.PlotDropoutRateHeterogeneity(params) ```

### Example output

```Loading required package: hypergeo
[,1]       [,2]       [,3]       [,4]       [,5]      [,6]
x.axis.ticks     0 0.00835456 0.01670912 0.02506368 0.03341824 0.0417728
heterogeneity  Inf 4.43749411 3.79826161 3.45024208 3.21112606 3.0284529
[,7]       [,8]       [,9]      [,10]     [,11]      [,12]
x.axis.ticks  0.05012736 0.05848192 0.06683648 0.07519104 0.0835456 0.09190016
heterogeneity 2.88009661 2.75472288 2.64577960 2.54915080 2.4620883 2.38266926
[,13]     [,14]     [,15]     [,16]    [,17]     [,18]
x.axis.ticks  0.1002547 0.1086093 0.1169638 0.1253184 0.133673 0.1420275
heterogeneity 2.3094977 2.2415291 2.1779623 2.1181696 2.061651 2.0079996
[,19]     [,20]     [,21]     [,22]     [,23]     [,24]
x.axis.ticks  0.1503821 0.1587366 0.1670912 0.1754458 0.1838003 0.1921549
heterogeneity 1.9568839 1.9080271 1.8611968 1.8161962 1.7728571 1.7310346
[,25]    [,26]     [,27]     [,28]     [,29]     [,30]
x.axis.ticks  0.2005094 0.208864 0.2172186 0.2255731 0.2339277 0.2422822
heterogeneity 1.6906030 1.651453 1.6134869 1.5766210 1.5407796 1.5058954
[,31]     [,32]     [,33]     [,34]    [,35]     [,36]
x.axis.ticks  0.2506368 0.2589914 0.2673459 0.2757005 0.284055 0.2924096
heterogeneity 1.4719083 1.4387643 1.4064148 1.3748157 1.343927 1.3137130
[,37]     [,38]     [,39]     [,40]     [,41]    [,42]
x.axis.ticks  0.3007642 0.3091187 0.3174733 0.3258278 0.3341824 0.342537
heterogeneity 1.2841397 1.2551772 1.2267977 1.1989756 1.1716873 1.144911
[,43]     [,44]     [,45]     [,46]     [,47]     [,48]
x.axis.ticks  0.3508915 0.3592461 0.3676006 0.3759552 0.3843098 0.3926643
heterogeneity 1.1186272 1.0928167 1.0674624 1.0425484 1.0180597 0.9939825
[,49]     [,50]     [,51]     [,52]     [,53]     [,54]
x.axis.ticks  0.4010189 0.4093734 0.4177280 0.4260826 0.4344371 0.4427917
heterogeneity 0.9703038 0.9470115 0.9240943 0.9015416 0.8793436 0.8574909
[,55]     [,56]     [,57]     [,58]     [,59]     [,60]
x.axis.ticks  0.4511462 0.4595008 0.4678554 0.4762099 0.4845645 0.4929190
heterogeneity 0.8359748 0.8147872 0.7939204 0.7733671 0.7531206 0.7331746
[,61]     [,62]     [,63]     [,64]     [,65]     [,66]
x.axis.ticks  0.5012736 0.5096282 0.5179827 0.5263373 0.5346918 0.5430464
heterogeneity 0.7135229 0.6941601 0.6750807 0.6562799 0.6377529 0.6194954
[,67]     [,68]     [,69]     [,70]     [,71]     [,72]
x.axis.ticks  0.5514010 0.5597555 0.5681101 0.5764647 0.5848192 0.5931738
heterogeneity 0.6015032 0.5837724 0.5662995 0.5490810 0.5321138 0.5153950
[,73]     [,74]     [,75]     [,76]     [,77]     [,78]
x.axis.ticks  0.6015283 0.6098829 0.6182375 0.6265920 0.6349466 0.6433011
heterogeneity 0.4989218 0.4826916 0.4667022 0.4509513 0.4354371 0.4201576
[,79]     [,80]     [,81]     [,82]     [,83]     [,84]
x.axis.ticks  0.6516557 0.6600103 0.6683648 0.6767194 0.6850739 0.6934285
heterogeneity 0.4051113 0.3902968 0.3757127 0.3613581 0.3472318 0.3333333
[,85]     [,86]     [,87]     [,88]     [,89]     [,90]
x.axis.ticks  0.7017831 0.7101376 0.7184922 0.7268467 0.7352013 0.7435559
heterogeneity 0.3196619 0.3062171 0.2929988 0.2800068 0.2672413 0.2547027
[,91]    [,92]     [,93]     [,94]     [,95]     [,96]
x.axis.ticks  0.7519104 0.760265 0.7686195 0.7769741 0.7853287 0.7936832
heterogeneity 0.2423913 0.230308 0.2184537 0.2068294 0.1954366 0.1842770
[,97]     [,98]     [,99]    [,100]
x.axis.ticks  0.8020378 0.8103923 0.8187469 0.8271015
heterogeneity 0.1733524 0.1626651 0.1522176 0.1420128
[,1]        [,2]       [,3]       [,4]       [,5]       [,6]
x.axis.ticks     0 0.008846886 0.01769377 0.02654066 0.03538754 0.04423443
heterogeneity    0 0.818603214 1.01592281 1.14648389 1.24435334 1.32195876
[,7]      [,8]       [,9]      [,10]      [,11]      [,12]
x.axis.ticks  0.05308132 0.0619282 0.07077509 0.07962198 0.08846886 0.09731575
heterogeneity 1.38544260 1.4383605 1.48298499 1.52087186 1.55314108 1.58063090
[,13]     [,14]     [,15]     [,16]     [,17]     [,18]
x.axis.ticks  0.1061626 0.1150095 0.1238564 0.1327033 0.1415502 0.1503971
heterogeneity 1.6039882 1.6237250 1.6402549 1.6539181 1.6649983 1.6737358
[,19]     [,20]     [,21]     [,22]     [,23]     [,24]
x.axis.ticks  0.159244 0.1680908 0.1769377 0.1857846 0.1946315 0.2034784
heterogeneity 1.680336 1.6849758 1.6878104 1.6889755 1.6885914 1.6867653
[,25]     [,26]    [,27]     [,28]     [,29]     [,30]
x.axis.ticks  0.2123253 0.2211722 0.230019 0.2388659 0.2477128 0.2565597
heterogeneity 1.6835931 1.6791615 1.673549 1.6668265 1.6590596 1.6503080
[,31]     [,32]     [,33]     [,34]     [,35]    [,36]
x.axis.ticks  0.2654066 0.2742535 0.2831004 0.2919472 0.3007941 0.309641
heterogeneity 1.6406268 1.6300670 1.6186757 1.6064970 1.5935717 1.579938
[,37]     [,38]     [,39]     [,40]     [,41]     [,42]
x.axis.ticks  0.3184879 0.3273348 0.3361817 0.3450286 0.3538754 0.3627223
heterogeneity 1.5656327 1.5506887 1.5351384 1.5190118 1.5023375 1.4851425
[,43]     [,44]    [,45]     [,46]     [,47]     [,48]
x.axis.ticks  0.3715692 0.3804161 0.389263 0.3981099 0.4069568 0.4158037
heterogeneity 1.4674527 1.4492927 1.430686 1.4116545 1.3922203 1.3724039
[,49]     [,50]     [,51]     [,52]     [,53]    [,54]
x.axis.ticks  0.4246505 0.4334974 0.4423443 0.4511912 0.4600381 0.468885
heterogeneity 1.3522250 1.3317029 1.3108559 1.2897019 1.2682582 1.246541
[,55]     [,56]     [,57]     [,58]     [,59]     [,60]
x.axis.ticks  0.4777319 0.4865787 0.4954256 0.5042725 0.5131194 0.5219663
heterogeneity 1.2245679 1.2023534 1.1799133 1.1572627 1.1344162 1.1113881
[,61]     [,62]     [,63]     [,64]     [,65]     [,66]
x.axis.ticks  0.5308132 0.5396601 0.5485069 0.5573538 0.5662007 0.5750476
heterogeneity 1.0881926 1.0648434 1.0413541 1.0177380 0.9940083 0.9701779
[,67]     [,68]     [,69]     [,70]    [,71]     [,72]
x.axis.ticks  0.5838945 0.5927414 0.6015883 0.6104352 0.619282 0.6281289
heterogeneity 0.9462598 0.9222665 0.8982108 0.8741051 0.849962 0.8257937
[,73]     [,74]     [,75]     [,76]     [,77]     [,78]
x.axis.ticks  0.6369758 0.6458227 0.6546696 0.6635165 0.6723634 0.6812102
heterogeneity 0.8016127 0.7774313 0.7532620 0.7291172 0.7050094 0.6809511
[,79]     [,80]     [,81]     [,82]     [,83]     [,84]
x.axis.ticks  0.6900571 0.6989040 0.7077509 0.7165978 0.7254447 0.7342916
heterogeneity 0.6569550 0.6330339 0.6092008 0.5854689 0.5618515 0.5383622
[,85]     [,86]     [,87]     [,88]     [,89]     [,90]
x.axis.ticks  0.7431384 0.7519853 0.7608322 0.7696791 0.7785260 0.7873729
heterogeneity 0.5150149 0.4918240 0.4688039 0.4459698 0.4233371 0.4009218
[,91]     [,92]     [,93]     [,94]     [,95]     [,96]
x.axis.ticks  0.7962198 0.8050666 0.8139135 0.8227604 0.8316073 0.8404542
heterogeneity 0.3787406 0.3568108 0.3351506 0.3137789 0.2927156 0.2719820
[,97]     [,98]     [,99]    [,100]
x.axis.ticks  0.8493011 0.8581480 0.8669949 0.8758417
heterogeneity 0.2516004 0.2315949 0.2119912 0.1928171
```

BTYD documentation built on Nov. 18, 2021, 1:10 a.m.