# Raised cosine distribution

Template:Probability distribution
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 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

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

## See also

## References

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