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Date: 3-4-2021
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Date: 5-4-2021
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Date: 11-2-2021
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The distribution with probability density function and distribution function
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(1) |
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(2) |
for and parameter
.
It is implemented in the Wolfram Language as RayleighDistribution[s].
The raw moments are given by
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(3) |
where is the gamma function, giving the first few as
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(4) |
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(5) |
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(6) |
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(7) |
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(8) |
The central moments are therefore
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(9) |
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(10) |
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(11) |
The mean, variance, skewness, and kurtosis excess are
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(12) |
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(13) |
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(14) |
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(15) |
The characteristic function is
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(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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