Built-in Mathematica Symbol

InverseGammaDistribution

,

]
represents an inverse gamma distribution with shape parameter

and scale parameter

.

The inverse gamma distribution InverseGammaDistribution[, ] is the distribution followed by the inverse of a GammaDistribution[, 1/] distributed random variable. »

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

The mean and variance of an inverse gamma distribution:

Probability density function:

The mean and variance of an inverse gamma distribution:

Probability density function:

Generate a set of pseudorandom numbers that are inverse gamma distributed:

Properties based on higher-order moments:

Third moment of an inverse gamma distribution:

The 0.75 quantile of an inverse 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:

InverseGammaDistribution 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: