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NakagamiDistribution

NakagamiDistribution
represents a Nakagami distribution with shape parameter and spread parameter .
  • The probability density for value is proportional to for , and is zero for .
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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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:
Closed form for symbolic order:
Closed form for symbolic order:
Hazard function:
Quantile function:
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 , is the energy per symbol, and is the spectral density of white noise:
Show that is a GammaDistribution:
Find the moment generating function (MGF):
Find the mean and the MGF in terms of the mean:
Find the amount of fading:
Parameter influence on the CDF for each :
Nakagami distribution is closed under scaling by a positive factor:
Relationships to other distributions:
RayleighDistribution is a special case of Nakagami distribution:
HoytDistribution is related to Nakagami distribution:
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