Probability density function
Note: b=0.4, β=3
Cumulative distribution function
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.
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.
The cumulative distribution function of the Gamma/Gompertz distribution is:
The moment generating function is given by:
where is a Hypergeometric function.
The Gamma/Gompertz distribution is a flexible distribution that can be skewed to the right or to the left.