Built-in Mathematica Symbol

FRatioDistribution

FRatioDistribution[n, m]
represents an F-ratio distribution with n numerator and m denominator degrees of freedom.

The probability density for value x in an F-ratio distribution is proportional to for , and is zero for . »

For integer n and m, the F-ratio distribution gives the distribution of the ratio of variances for samples from normal distributions.

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

The mean and variance of an F-ratio distribution:

The probability density function is related to the beta function:

The mean and variance of an F-ratio distribution:

The probability density function is related to the beta function:

Generate a set of pseudorandom numbers that have the F-ratio distribution:

Properties based on higher-order moments:

The fourth moment of a particular F-ratio distribution is finite:

However, some F-ratio distributions are too heavy-tailed to have fourth moments:

The 0.75 quantile of an F-ratio distribution with

and

:

Compute the p-value for an F-test with n and m degrees of freedom:

Plot the cumulative distribution function of an F-ratio distribution:

A contour plot as both x and m are varied:

The probability density function integrates to unity:

Moments can be obtained from the characteristic function:

FRatioDistribution is not defined when n or m is not a positive real number:

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