Raised cosine distribution
Probability density function
Cumulative distribution function
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.
The pdf of the raised cosine distribution is a solution to the following differential equation:
- Horst Rinne (2010). "Location-Scale Distributions - Linear Estimation and Probability Plotting Using MATLAB" (PDF). p. 116. Retrieved 2012-11-16.