BUILT-IN MATHEMATICA SYMBOL

# NoncentralFRatioDistribution

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

NoncentralFRatioDistribution[n, m, , ]
represents a doubly noncentral F-ratio distribution with numerator noncentrality parameter and denominator noncentrality parameter .

## DetailsDetails

• The noncentral F-ratio distribution is the distribution of the ratio of a noncentral random variable and a random variable divided by their respective degrees of freedom.
• The doubly noncentral F-ratio distribution is the distribution of a ratio of two noncentral -distributed random variables divided by their respective degrees of freedom.
• NoncentralFRatioDistribution allows n, m, , and to be any positive real numbers.
• NoncentralFRatioDistribution can be used with such functions as Mean, CDF, and RandomVariate.

## ExamplesExamplesopen allclose all

### Basic Examples (5)Basic Examples (5)

Probability density function:

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Probability density function for a doubly noncentral F-ratio distribution:

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Cumulative distribution function:

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Cumulative distribution function for a doubly noncentral F-ratio distribution:

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Mean and variance:

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Mean and variance for doubly noncentral:

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