BUILT-IN MATHEMATICA SYMBOL

NakagamiDistribution

represents a Nakagami distribution with shape parameter

and spread parameter

.

MORE INFORMATION

NakagamiDistribution is also known as Nakagami- distribution.

The probability density for value is proportional to for , and is zero for .

NakagamiDistribution allows and to be any positive real numbers.

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

EXAMPLES

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Basic Examples (4)

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 are Nakagami distributed:

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 depends only on the first parameter:

Limiting values:

Kurtosis depends only on the first parameter:

Limiting values:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

Closed form for symbolic order:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

Applications (1)

In the theory of fading channels, NakagamiDistribution is used to model fading amplitude for land-mobile and indoor-mobile multipath propagation and also in the presence of ionospheric scintillation. Find the distribution of instantaneous signal-to-noise ratio where