Gamma/Gompertz distribution

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Gamma/Gompertz distribution
Probability density function
Gamma Gompertz cumulative distribution
Note: b=0.4, β=3
Cumulative distribution function
Gamma Gompertz cumulative distribution
Parameters
Support
PDF
CDF
Mean
           

           
Median
Mode
Variance
           








MGF



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[edit]

Probability density function[edit]

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[edit]

The cumulative distribution function of the Gamma/Gompertz distribution is:

Moment generating function[edit]

The moment generating function is given by:

where is a Hypergeometric function.

Properties[edit]

The Gamma/Gompertz distribution is a flexible distribution that can be skewed to the right or to the left.

Related distributions[edit]

  • 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 [1]
  • 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.[1]

See also[edit]

Notes[edit]

  1. ^ a b Bemmaor, A.C.; Glady, N. (2012)

References[edit]