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)

## Arguments

r shape parameter of the Gamma distribution of the purchase process. The smaller r, the stronger the heterogeneity of the purchase process shape parameter of the Gamma distribution for the lifetime process. The smaller s, the stronger the heterogeneity of customer lifetimes rate parameter of the Gamma distribution of the purchase process rate 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

## Value

Returns the expected transaction values according to the chosen model.

## References

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.