# bgbb.PlotDropoutRateHeterogeneity: BG/BB Plot Dropout Rate Heterogeneity In BTYD: Implementing BTYD Models with the Log Sum Exp Patch

## Description

Plots and returns the estimated beta distribution of Theta (customers' propensities to drop out).

## Usage

 `1` ```bgbb.PlotDropoutRateHeterogeneity(params) ```

## Arguments

 `params` BG/BB parameters - a vector with alpha, beta, gamma, and delta, in that order. Alpha and beta are unobserved parameters for the beta-Bernoulli transaction process. Gamma and delta are unobserved parameters for the beta-geometric dropout process.

## Details

This returns the distribution of each customer's geometric parameter that determines their lifetime (using the BG/BB assumption that a customer's lifetime can be modeled with a geometric distribution).

## Value

Distribution of customers' propensities to drop out.

## Examples

 ```1 2 3 4``` ```params <- c(1.2, 0.75, 0.66, 2.78) bgbb.PlotDropoutRateHeterogeneity(params) params <- c(0.2, 1.5, 3.2, 6) bgbb.PlotDropoutRateHeterogeneity(params) ```

### Example output

```Loading required package: hypergeo
[1]          Inf 6.4965179162 5.0405997124 4.3120367595 3.8387726494
[6] 3.4925948562 3.2214110821 2.9992751477 2.8115235862 2.6491174856
[11] 2.5061188374 2.3784317461 2.2631197093 2.1580103536 2.0614542703
[16] 1.9721713879 1.8891495066 1.8115751941 1.7387854589 1.6702331665
[21] 1.6054617849 1.5440866083 1.4857805726 1.4302633847 1.3772930824
[26] 1.3266594044 1.2781785260 1.2316888369 1.1870475257 1.1441277930
[31] 1.1028165596 1.0630125692 1.0246248065 0.9875711705 0.9517773547
[36] 0.9171758985 0.8837053771 0.8513097080 0.8199375550 0.7895418120
[41] 0.7600791558 0.7315096565 0.7037964371 0.6769053745 0.6508048371
[46] 0.6254654528 0.6008599037 0.5769627437 0.5537502370 0.5312002128
[51] 0.5092919367 0.4880059944 0.4673241877 0.4472294413 0.4277057178
[56] 0.4087379423 0.3903119329 0.3724143389 0.3550325839 0.3381548145
[61] 0.3217698541 0.3058671600 0.2904367857 0.2754693448 0.2609559805
[66] 0.2468883355 0.2332585268 0.2200591211 0.2072831144 0.1949239118
[71] 0.1829753110 0.1714314868 0.1602869781 0.1495366757 0.1391758136
[76] 0.1291999602 0.1196050131 0.1103871945 0.1015430493 0.0930694458
[81] 0.0849635775 0.0772229694 0.0698454860 0.0628293436 0.0561731277
[86] 0.0498758144 0.0439368001 0.0383559387 0.0331335907 0.0282706876
[91] 0.0237688156 0.0196303294 0.0158585074 0.0124577698 0.0094339973
[96] 0.0067950174 0.0045513953 0.0027178372 0.0013160322 0.0003818863
[101] 0.0000000000
[1] 0.000000e+00 8.071149e-03 3.524973e-02 8.171181e-02 1.460991e-01
[6] 2.265225e-01 3.208717e-01 4.269626e-01 5.426209e-01 6.657327e-01
[11] 7.942769e-01 9.263462e-01 1.060160e+00 1.194073e+00 1.326580e+00
[16] 1.456313e+00 1.582049e+00 1.702697e+00 1.817306e+00 1.925052e+00
[21] 2.025235e+00 2.117275e+00 2.200707e+00 2.275172e+00 2.340411e+00
[26] 2.396259e+00 2.442639e+00 2.479556e+00 2.507088e+00 2.525380e+00
[31] 2.534640e+00 2.535132e+00 2.527167e+00 2.511100e+00 2.487326e+00
[36] 2.456269e+00 2.418381e+00 2.374138e+00 2.324030e+00 2.268562e+00
[41] 2.208247e+00 2.143601e+00 2.075142e+00 2.003384e+00 1.928837e+00
[46] 1.851997e+00 1.773354e+00 1.693378e+00 1.612526e+00 1.531234e+00
[51] 1.449918e+00 1.368971e+00 1.288763e+00 1.209639e+00 1.131918e+00
[56] 1.055893e+00 9.818303e-01 9.099685e-01 8.405188e-01 7.736653e-01
[61] 7.095649e-01 6.483479e-01 5.901183e-01 5.349550e-01 4.829118e-01
[66] 4.340193e-01 3.882850e-01 3.456955e-01 3.062167e-01 2.697962e-01
[71] 2.363640e-01 2.058343e-01 1.781070e-01 1.530694e-01 1.305978e-01
[76] 1.105590e-01 9.281230e-02 7.721082e-02 6.360349e-02 5.183648e-02
[81] 4.175489e-02 3.320431e-02 2.603229e-02 2.008981e-02 1.523259e-02
[86] 1.132237e-02 8.228036e-03 5.826645e-03 4.004308e-03 2.656934e-03
[91] 1.690803e-03 1.022970e-03 5.814904e-04 3.054303e-04 1.446761e-04
[96] 5.951156e-05 1.995520e-05 4.844662e-06 6.525394e-07 2.085244e-08
[101] 0.000000e+00
```

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