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BeckmannDistribution

BeckmannDistribution
represents the Beckmann distribution with means and and standard deviations and .
BeckmannDistribution
represents the Beckmann distribution with means and , standard deviations and , and correlation .
  • BeckmannDistribution allows to be any real numbers, any positive real numbers, and any number between -1 and 1.
Probability density function:
Cumulative distribution function:
Probability density function:
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Cumulative distribution function:
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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:
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