In probability and statistics, the Gamma/Gompertz distribution is a continuous probability distribution. It has been used as an aggregate-level model of customer lifetime and a model of mortality risks. Specification Probability density function The probability density function of the Gamma/Gompertz distribution is: where is the scale parameter and are the shape parameters of the Gamma/Gompertz distribution. Cumulative distribution function The cumulative distribution function of the Gamma/Gompertz distribution is: Moment generating function The moment generating function is given by: where is a Hypergeometric function. Properties The Gamma/Gompertz distribution is a flexible distribution that can be skewed to the right or to the left. Related distributions When β = 1, this reduces to an Exponential distribution with parameter sb. The gamma distribution is a natural conjugate prior to a Gompertz likelihood with known, scale parameter When the shape parameter of a Gompertz distribution varies according to a gamma distribution with shape parameter and scale parameter (mean = ), the distribution of is Gamma/Gompertz. See also Gompertz distribution Customer lifetime value Notes References Continuous distributions hu:Gompertz-eloszlás