(real) In probability theory and statistics, the raised cosine distribution is a continuous probability distribution supported on the interval

The probability density function (PDF) is and zero otherwise.

The cumulative distribution function (CDF) is 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

Because the standard raised cosine distribution is an even function, the odd moments are zero.