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Raised cosine distribution

From Wikipedia, the free encyclopedia

Raised cosine
Probability density function
Plot of the raised cosine PDF

Cumulative distribution function
Plot of the raised cosine CDF

Parameters

(real)

(real)
Support
PDF
CDF
Mean
Median
Mode
Variance
Skewness
Ex. kurtosis
MGF
CF

In probability theory and statistics, the raised cosine distribution is a continuous probability distribution supported on the interval . The probability density function (PDF) is

for and zero otherwise. The cumulative distribution function (CDF) is

for and zero for and unity for .

The moments of the raised cosine distribution are somewhat complicated in the general case, but are considerably simplified for the standard raised cosine distribution. The standard raised cosine distribution is just the raised cosine distribution with and . Because the standard raised cosine distribution is an even function, the odd moments are zero. The even moments are given by:

where is a generalized hypergeometric function.

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Transcription

See also

References

  • Horst Rinne (2010). "Location-Scale Distributions – Linear Estimation and Probability Plotting Using MATLAB" (PDF). p. 116. Retrieved 2012-11-16.
This page was last edited on 29 December 2020, at 11:50
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