Built-in Mathematica Symbol

NoncentralFRatioDistribution

]
represents a noncentral F-ratio distribution with n numerator degrees of freedom and m denominator degrees of freedom and numerator noncentrality parameter

.

MORE INFORMATION

The noncentral F-ratio distribution is the distribution of the ratio of a noncentral random variable and a random variable.

NoncentralFRatioDistribution allows n, m, and to be any positive real numbers.

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

EXAMPLES

CLOSE ALL

Basic Examples (2)

The mean and variance of a noncentral F-ratio distribution:

The probability density function of the noncentral F-ratio distribution:

The mean and variance of a noncentral F-ratio distribution:

The probability density function of the noncentral F-ratio distribution:

Scope (3)

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

Properties based on higher-order moments:

The 0.75 quantile of a noncentral F-ratio distribution:

Applications (1)

Plot the cumulative distribution function of the random variable:

Properties & Relations (2)

The probability density function integrates to unity:

NoncentralFRatioDistribution[n, m, 0] is equivalent to FRatioDistribution[n, m]:

Possible Issues (4)

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

NoncentralFRatioDistribution is not defined when

is not a positive real number:

The characteristic function of a noncentral F-ratio distribution has no closed-form representation:

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