ShiftedBetaGeometric#
- class pymc_marketing.clv.distributions.ShiftedBetaGeometric(name, *args, **kwargs)[source]#
Shifted Beta-Geometric distribution.
This mixture distribution extends the Geometric distribution to support heterogeneity across observations.
Hardie and Fader describe this distribution with the following PMF and survival functions in [1]:
\[\begin{split}\begin{aligned} \mathbb{P}(T=t \mid \alpha,\beta) &= \frac{B(\alpha+1,\beta+t-1)}{B(\alpha,\beta)}, \quad t=1,2,\dots \\ \mathbb{S}(t \mid \alpha,\beta) &= \frac{B(\alpha,\beta+t)}{B(\alpha,\beta)}, \quad t=1,2,\dots \end{aligned}\end{split}\]Support
\(t \in \mathbb{N}_{>0}\)
- Parameters:
- alphatensor_like of
float Scale parameter (alpha > 0).
- betatensor_like of
float Scale parameter (beta > 0).
- alphatensor_like of
References
[1]Fader, P. S., & Hardie, B. G. (2007). How to project customer retention. Journal of Interactive Marketing, 21(1), 76-90. https://faculty.wharton.upenn.edu/wp-content/uploads/2012/04/Fader_hardie_jim_07.pdf
Methods
ShiftedBetaGeometric.__init__(*args, **kwargs)ShiftedBetaGeometric.dist(alpha, beta, ...)Create a tensor variable corresponding to the
clsdistribution.ShiftedBetaGeometric.logcdf(alpha, beta)Adapted from Expression (6) on p.6 of Fader & Hardie (2007).
ShiftedBetaGeometric.logp(alpha, beta)From Expression (5) on p.6 of Fader & Hardie (2007).
ShiftedBetaGeometric.support_point(size, ...)Calculate a reasonable starting point for sampling.
Attributes