FisherZDistribution

FisherZDistribution[n,m]

represents a Fisher distribution with n numerator and m denominator degrees of freedom.

Details

Background & Context

Examples

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Basic Examples  (4)

Probability density function:

Cumulative distribution function:

Mean:

Median:

Scope  (7)

Generate a sample of pseudorandom numbers from a Fisher 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:

Kurtosis:

Different moments with closed forms as functions of parameters, including Moment:

CentralMoment:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

Applications  (1)

Given a binormal sample, the -statistic follows a shifted FisherZDistribution:

Generate the distribution of -statistics for binormal samples of size :

Visually compare the -statistic distribution to a shifted FisherZDistribution:

DistributionFitTest confirms the result:

Properties & Relations  (2)

Relationships to other distributions:

Fisher distribution is a transformation of FRatioDistribution:

Neat Examples  (1)

PDFs for different n values with CDF contours:

Introduced in 2010
 (8.0)
 |
Updated in 2016
 (10.4)