BUILT-IN MATHEMATICA SYMBOL

NoncentralBetaDistribution

represents a noncentral beta distribution with shape parameters

,

and noncentrality parameter

.

MORE INFORMATION

The probability density for value in a noncentral beta distribution is proportional to for , and is zero for or .

NoncentralBetaDistribution allows , , and to be any positive real numbers.

NoncentralBetaDistribution can be used with such functions as Mean, CDF, and RandomVariate.

EXAMPLES

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Basic Examples (3)

Probability density function:

Cumulative distribution function:

Mean and variance:

Probability density function:

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Cumulative distribution function:

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Mean and variance:

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Scope (6)

Generate a set of pseudorandom numbers that are beta distributed:

Compare the histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare a density histogram of the sample with the PDF of the estimated distribution:

Skewness:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

Applications (1)

Plot the survival function of a noncentral beta distribution as a function of the noncentrality parameter:

Properties & Relations (5)

Parameter influence on the CDF for each

:

Relationships to other distributions:

With noncentrality parameter

going to 0, this is BetaDistribution:

NoncentralBetaDistribution is a transformation of NoncentralFRatioDistribution:

NoncentralBetaDistribution can be obtained as a transformation of ChiSquareDistribution and NoncentralChiSquareDistribution: