ggomnbd_expectation {CLVTools}

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.