This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# KDistribution

 KDistribution represents a K distribution with shape parameters and w.
• The probability density for value in a K distribution is proportional to for and otherwise.
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   (7)
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:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (1)
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: