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.
pnbd_nocov_expectation(r, s, alpha_0, beta_0, vT_i) pnbd_staticcov_expectation(r, s, vAlpha_i, vBeta_i, vT_i)
| r | shape parameter of the Gamma distribution of the purchase process. The smaller r, the stronger the heterogeneity of the purchase process |
|---|---|
| s | shape parameter of the Gamma distribution for the lifetime process. The smaller s, the stronger the heterogeneity of customer lifetimes |
| alpha_0 | scale parameter of the Gamma distribution of the purchase process |
| 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 |
Returns the expected transaction values according to the chosen model.
Schmittlein DC, Morrison DG, Colombo R (1987). “Counting Your Customers: Who-Are They and What Will They Do Next?” Management Science, 33(1), 1–24.
Fader PS, Hardie BGS (2005). “A Note on Deriving the Pareto/NBD Model and Related Expressions.” URL http://www.brucehardie.com/notes/009/pareto_nbd_derivations_2005-11-05.pdf.
Fader PS, Hardie BG (2007). “Incorporating time-invariant covariates into the Pareto/NBD and BG/NBD models.” URL http://www.brucehardie.com/notes/019/time_invariant_covariates.pdf.