ggomnbd_expectation: GGompertz/NBD: Unconditional Expectation

In CLVTools: Tools for Customer Lifetime Value Estimation

GGompertz/NBD: Unconditional Expectation

Description

Computes the expected number of repeat transactions in the interval (0, vT_i] for a randomly selected customer, where 0 is defined as the point when the customer came alive.

Usage

ggomnbd_nocov_expectation(r, alpha_0, b, s, beta_0, vT_i)

ggomnbd_staticcov_expectation(r, b, s, vAlpha_i, vBeta_i, vT_i)

Arguments

r	shape parameter of the Gamma distribution of the purchase process. The smaller r, the stronger the heterogeneity of the purchase process.
alpha_0	scale parameter of the Gamma distribution of the purchase process.
b	scale parameter of the Gompertz distribution (constant across customers)
s	shape parameter of the Gamma distribution for the lifetime process The smaller s, the stronger the heterogeneity of customer lifetimes.
beta_0	scale parameter for the Gamma distribution for the lifetime process
vT_i	Number of periods since the customer came alive
vAlpha_i	Vector of individual parameters alpha
vBeta_i	Vector of individual parameters beta

Value

Returns the expected transaction values according to the chosen model.

References

Bemmaor AC, Glady N (2012). “Modeling Purchasing Behavior with Sudden “Death”: A Flexible Customer Lifetime Model” Management Science, 58(5), 1012-1021.

Adler J (2022). “Comment on “Modeling Purchasing Behavior with Sudden “Death”: A Flexible Customer Lifetime Model” Management Science 69(3):1929-1930.

The expression for the PMF was derived by Adler J (2024). (unpublished)

CLVTools documentation built on Oct. 13, 2024, 9:07 a.m.