SuzukiDistribution

Generate a set of pseudorandom numbers that are Suzuki distributed:

Compare 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 second parameter:

Skewness is an increasing function with limiting values:

Kurtosis depends only on the second parameter:

Kurtosis is an increasing function with limiting values:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

FactorialMoment:

Cumulant:

Hazard function does not have closed form but can be evaluated numerically:

Quantile function:

In the theory of fading channels, SuzukiDistribution 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:

Find the mean:

Find the amount of fading:

Limiting values:

Parameter influence on the CDF for each :

Suzuki distribution is closed under scaling by a positive factor:

SuzukiDistribution is a parameter mixture of RayleighDistribution and LogNormalDistribution:

Suzuki distribution can be obtained from RayleighDistribution and LogNormalDistribution: