KDistribution

Generate a set of pseudorandom numbers that are K distributed:

Compare its 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 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:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

In the theory of fading channels, KDistribution is used to model fading amplitude. Find the distribution of instantaneous signal-to-noise ratio where , is the energy per symbol, and is the spectral density of white noise:

The probability density function:

Find the moment-generating function (MGF):

Find the mean:

Express the MGF in terms of the mean:

Find the amount of fading:

Limiting values:

Parameter influence on the CDF for each :

K distribution is closed under scaling by a positive factor:

KDistribution can be obtained from ExponentialDistribution and GammaDistribution:

KDistribution can be represented as a parameter mixture of RayleighDistribution and GammaDistribution: