Raised cosine distribution

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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, 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.

Differential equation[edit]

The pdf of the raised cosine distribution is a solution to the following differential equation:

See also[edit]

References[edit]