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

# HoytDistribution

 HoytDistribution represents a Hoyt distribution with shape parameter q and spread parameter .
• The probability density for value is proportional to for , and is zero for .
• HoytDistribution allows q to be any number between 0 and 1, and to be any positive real number.
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 Hoyt 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, HoytDistribution is used to model fading amplitude on satellite links in the presence of strong scintillation due to ionosphere. Find the distribution of instantaneous signal-to-noise ratio where , is the energy per symbol, and is the spectral density of white noise:
Find the moment-generating function (MGF):
Find the mean:
Express the MGF in terms of the mean:
Parameter influence on the CDF for each :
Hoyt distribution family is closed under scaling by a positive factor:
Relationships to other distributions:
NakagamiDistribution is related to Hoyt distribution:
Hoyt distribution can be obtained from ExponentialDistribution and ArcSinDistribution:
Hoyt distribution can be obtained from BinormalDistribution:
Hoyt distribution is a special case of BeckmannDistribution:
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