BeckmannDistribution

Generate a set of pseudorandom numbers that are Beckmann distributed:

Compare the 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:

Hazard function:

Quantile function:

The length of a 2D vector with normally distributed and correlated components follows a Beckmann distribution:

Find the probability that a vector is longer than 1:

Find the average length of a vector:

Simulate possible lengths for a sample of 30 vectors:

In the theory of fading channels, BeckmannDistribution 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:

For standard normal distributions:

Special case Rayleigh fading:

Special case Rice fading:

Special case Hoyt fading:

Parameter influence on the CDF for each :

A Beckmann distribution is closed under scaling by a positive number:

Relationships to other distributions:

For a Beckmann distribution simplifies to an uncorrelated case:

Beckmann distribution is related to NoncentralChiSquareDistribution:

The norm of the vector of two components from NormalDistribution has a Beckmann distribution:

Beckmann distribution is related to BinormalDistribution:

HoytDistribution can be obtained from a Beckmann distribution:

RiceDistribution is a special case of a Beckmann distribution: