Rayleigh Distribution
المؤلف:
Papoulis, A
المصدر:
Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill
الجزء والصفحة:
pp. 104 and 148
13-4-2021
2593
Rayleigh Distribution
The distribution with probability density function and distribution function
for 
and parameter 
.
It is implemented in the Wolfram Language as RayleighDistribution[s].
The raw moments are given by
 |
(3)
|
where 
is the gamma function, giving the first few as
The central moments are therefore
The mean, variance, skewness, and kurtosis excess are
The characteristic function is
![phi(t)=1-sqrt(pi/2)ste^(-s^2t^2/2)[erfi((st)/(sqrt(2)))-i].](https://mathworld.wolfram.com/images/equations/RayleighDistribution/NumberedEquation2.gif) |
(16)
|
REFERENCES:
Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 104 and 148, 1984.
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