Built-in Mathematica Symbol

GammaDistribution

,

]
represents a gamma distribution with shape parameter

and scale parameter

.

The probability density for value x in a gamma distribution is proportional to for , and is zero for . »

GammaDistribution can be used with such functions as Mean, CDF and RandomReal. »

The mean and variance of a gamma distribution:

The probability density function of the gamma distribution depends on the Gamma function:

The mean and variance of a gamma distribution:

The probability density function of the gamma distribution depends on the Gamma function:

Generate a set of pseudorandom numbers that are gamma distributed:

Properties based on higher-order moments:

Third moment of a gamma distribution:

The 0.75 quantile of a gamma distribution with

and

:

Plot the cumulative distribution function of the random variable:

A contour plot as both x and

are varied:

The probability density function integrates to unity:

Moments can be obtained from the characteristic function:

GammaDistribution is not defined when either

or

is not a positive real number:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: