RiskGamma

Description

RiskGamma specifies a gamma distribution with shape parameter alpha and scale parameter beta. The Gamma distribution often represents the distribution of interarrival times for several events from a Poisson process. More generally, it can be used to model a nonnegative value when skewness is desired. In a Bayesian context, it can be used to represent the distribution of possible values for the rate of a Poisson process, based on observations of the process.

 

Examples

RiskGamma(2.5,1) returns a gamma distribution with shape parameter 2.5 and scale parameter 1.

RiskGamma(C12,C13) returns a gamma distribution with shape and scale parameters taken from cells C12 and C13.

 

Guidelines

alpha and beta must be positive.

Parameters

     continuous shape parameter      

     continuous scale parameter      

 

Domain

          continuous

Density and Cumulative Distribution Functions

Here, is the Gamma Function and is the Incomplete Gamma Function.

 

Mean

 

Variance

 

Skewness

 

Kurtosis

 

Mode

     if

0           if

Examples