Rayleigh distribution
Rayleigh distribution
[′rā·lē ‚dis·trə‚byü·shən]Rayleigh Distribution
The Rayleigh distribution of the probabilities of the random variable X is characterized by the probability density function
The distribution function is
The mathematical expectation is 
and the variance is DX = (4 - π)σ4/2. The maximum value of the density function is equal to 
and is reached when x= σ. Curves of the density function for various σ are shown in Figure 1.
The Rayleigh distribution is encountered in applications of probability theory to, for example, radio engineering. The distribution was introduced by Lord Rayleigh in 1880 in connection with the problem of interference of harmonic oscillations with spiral phases.