LogGamma distribution | Vose Software

LogGamma distribution

Format: LogGamma(
a, b, l)


A Variable X is LogGamma distributed if its natural log is Gamma distributed. In ModelRisk we include an extra minimum parameter l because a standard LogGamma distribution has (rather inconveniently) a minimum value of 1 when the Gamma variable = 0. Thus:

LogGamma(a, β, l) = EXP[Gamma(a, β)] +(l-1)


The LogGamma distribution is sometimes used to model the distribution of claim size in insurance. Set l= 1 to get the standard LogGamma(a, β) distribution.

ModelRisk functions added to Microsoft Excel for the LogGamma distribution

VoseLogGamma generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseLogGammaObject constructs a distribution object for this distribution.

VoseLogGammaProb returns the probability density or cumulative distribution function for this distribution.

VoseLogGammaProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseLogGammaFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseLogGammaFitObject constructs a distribution object of this distribution fitted to data.

VoseLogGammaFitP returns the parameters of this distribution fitted to data.


LogGamma distribution equations