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based on an earlier version of the Wolfram Language.
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# FRatioDistribution

 FRatioDistribution represents an F-ratio distribution with n numerator and m denominator degrees of freedom.
• The probability density for value 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.
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (7)
Generate a set of pseudorandom numbers that have the F-ratio distribution:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the density histogram of the sample with the PDF of the estimated distribution:
Skewness varies with the degrees of freedom:
Limiting value:
Kurtosis varies with the degrees of freedom:
Limiting value is the kurtosis of NormalDistribution:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (1)
FRatioDistribution is the distribution of the ratio of two sample variances drawn from two normal distributions. Define the Fisher ratio statistic:
Generate 1000 batches of samples from two standard normal distributions:
Compute values of the Fisher ratio statistics for each batch:
Find the -value of the Fisher ratio test for the first batch:
Compare with FisherRatioTest:
Parameter influence on the CDF for each :
Relationships to other distributions:
ChiSquareDistribution is a limiting case of F-ratio distribution:
F-ratio is the ratio of two ChiSquareDistribution variables:
F-ratio distribution can be obtained from BetaDistribution:
A square of StudentTDistribution has F-ratio distribution:
F-ratio distribution is the distribution of the inverse square of StudentTDistribution:
F-ratio distribution is a special case of type 6 PearsonDistribution:
FRatioDistribution is a transformation of Laplace distribution:
FisherZDistribution is a transformation of F-ratio distribution:
NoncentralFRatioDistribution simplifies to F-ratio distribution:
Doubly NoncentralFRatioDistribution simplifies to F-ratio distribution:
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:
New in 6