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.
ggomnbd_nocov_expectation(r, alpha_0, b, s, beta_0, vT_i)
ggomnbd_staticcov_expectation(r, b, s, vAlpha_i, vBeta_i, vT_i)shape parameter of the Gamma distribution of the purchase process. The smaller r, the stronger the heterogeneity of the purchase process.
scale parameter of the Gamma distribution of the purchase process.
scale parameter of the Gompertz distribution (constant across customers)
shape parameter of the Gamma distribution for the lifetime process The smaller s, the stronger the heterogeneity of customer lifetimes.
scale parameter for the Gamma distribution for the lifetime process
Number of periods since the customer came alive
Vector of individual parameters alpha
Vector of individual parameters beta
Returns the expected transaction values according to the chosen model.
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 (unpublished)