BG/NBD: Probability Mass Function (PMF)

Calculate P(X(t)=x), the probability that a randomly selected customer makes exactly x transactions in the interval (0, t].

bgnbd_nocov_PMF(r, alpha, a, b, x, vT_i)

bgnbd_staticcov_PMF(r, x, vAlpha_i, vA_i, vB_i, vT_i)

Arguments

r

shape parameter of the Gamma distribution of the purchase process

alpha

scale parameter of the Gamma distribution of the purchase process

a

shape parameter of the Beta distribution of the lifetime process

b

shape parameter of the Beta distribution of the lifetime process

x

The number of transactions to calculate the probability for (unsigned integer).

vT_i

Number of periods since the customer came alive.

vAlpha_i

Vector of individual parameters alpha

vA_i

Vector of individual parameters a

vB_i

Vector of individual parameters b

Value

Returns a vector of probabilities.

References

Fader PS, Hardie BGS, Lee KL (2005). ““Counting Your Customers” the Easy Way: An Alternative to the Pareto/NBD Model” Marketing Science, 24(2), 275-284.

Fader PS, Hardie BGS (2013). “Overcoming the BG/NBD Model's #NUM! Error Problem” URL http://brucehardie.com/notes/027/bgnbd_num_error.pdf.

Fader PS, Hardie BGS (2007). “Incorporating time-invariant covariates into the Pareto/NBD and BG/NBD models.” URL http://www.brucehardie.com/notes/019/time_invariant_covariates.pdf.

Fader PS, Hardie BGS, Lee KL (2007). “Creating a Fit Histogram for the BG/NBD Model” URL https://www.brucehardie.com/notes/014/bgnbd_fit_histogram.pdf