# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# GompertzMakehamDistribution

represents a Gompertz distribution with scale parameter λ and frailty parameter ξ.

GompertzMakehamDistribution[λ,ξ,θ,α]
represents a GompertzMakeham distribution with parameters λ, ξ, θ, and α.

## DetailsDetails

• The hazard function for value in a Gompertz distribution is given by for , and is zero for .
• The hazard function for value in a GompertzMakeham distribution is given by for and is zero for .
• GompertzMakehamDistribution allows λ and ξ to be any positive real numbers and θ and α any nonnegative real numbers.
• GompertzMakehamDistribution can be used with such functions as Mean, CDF, and RandomVariate.

## ExamplesExamplesopen allclose all

### Basic Examples  (6)Basic Examples  (6)

Probability density function of Gompertz distribution:

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Cumulative distribution function of Gompertz distribution:

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Probability density function of GompertzMakeham distribution:

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Cumulative distribution function of GompertzMakeham distribution:

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Mean and variance of a Gompertz distribution:

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Median of Gompertz distribution:

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