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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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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:
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:
Find the amount of fading:
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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