BetaGeoModel.expected_num_purchases_new_customer

BetaGeoModel.expected_num_purchases_new_customer(t)

Posterior expected number of purchases for any interval of length \(t\). See equation (9) of [1].

The customer_id shouldn’t matter too much here since no individual-specific data is conditioned on.

\[\mathbb{E}\left(X(t) \mid r, \alpha, a, b \right) = \frac{a + b - 1}{a - 1} \left[ 1 - \left(\frac{\alpha}{\alpha + t}\right)^r \text{hyp2f1}\left(r, b; a + b - 1; \frac{t}{\alpha + t}\right) \right]\]