ContContract

class pymc_marketing.clv.distributions.ContContract(name: str, *args, rng=None, dims: str | Sequence[str | None] | None = None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)

Distribution class of a continuous contractual data-generating process.

That is where purchases can occur at any time point (continuous) and churning/dropping out is explicit (contractual).

\[f(\lambda, p | d, x, t_1, \dots, t_x, T) = f(\lambda, p | t_x, T) = (1 - p)^{x-1} \lambda^x \exp(-\lambda t_x) p^d \left\{(1-p)\exp(-\lambda*(T - t_x))\right\}^{1 - d}\]

Support	\(t_j > 0\) for \(j = 1, \dots, x\)
Mean	\(\mathbb{E}[X(t) | \lambda, p, d] = \frac{1}{p} - \frac{1}{p}\exp\left(-\lambda p \min(t, T)\right)\)

Methods

ContContract.__init__(*args, **kwargs)
ContContract.dist(lam, p, T, **kwargs)	Get the distribution from the parameters.
ContContract.logp(lam, p, T)	Log-likelihood of the distribution.

Attributes

rv_op