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

BeckmannDistribution

 BeckmannDistribution represents the Beckmann distribution with means and and standard deviations and . BeckmannDistributionrepresents 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:
 Out[1]=
 Out[2]=
 Out[3]=

Cumulative distribution function:
 Out[1]=
 Out[2]=
 Out[3]=
 Scope   (4)
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:
 Applications   (2)
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:
For standard normal distributions: