I am learning to use BTYD package that uses Pareto/NBD model to predict when will be a customer is expected to be back. However, all literature on this model is full of mathematics and there does not appear to be a simple/conceptual explanation of the workings of this model. Is it possible to understand Pareto/NBD model for non-mathmeticians? I have gone through this famous paper by Fader . Pareto/NBD model makes the following assumptions:
i. While active, the number of transactions made by a customer in a time period of length t is distributed Poisson with transaction rate λ.
ii. Heterogeneity in transaction rates across customers follows a gamma distribution with shape parameter r and scale parameter α.
iii. Each customer has an unobserved “lifetime” of length τ. This point at which the customer becomes inactive is distributed exponential with dropout rate µ.
iv) Heterogeneity in dropout rates across customers follows a gamma distribution with shape parameter s and scale parameter β.
v. The transaction rate λ and the dropout rate µ vary independently across customers."
I do not understand the (intuition behind) rationale of assumptions (ii), (iii) and (iv). Why only these distributions, why not others?
Also BG/NBD model assumptions are:
i.) While active, the number of transactions made by a customer follows a Poisson process with transaction rate λ. This is equivalent to assuming that the time between transactions is distributed exponential with transaction rate λ
ii) Heterogeneity in λ follows a gamma distribution
iii) After any transaction, a customer becomes inactive with probability p. Therefore the point at which the customer “drops out” is distributed across transactions according to a (shifted) geometric distribution with pmf
iv) Heterogeneity in p follows a beta distribution
The (intuitive) rationality of assumptions (ii), (iii) and (iv) are also not at all obvious.
I shall be grateful for any help. Thanks.