Raised cosine distribution¶

mpsci.distributions.cosine.cdf(x)¶

Cumulative distribution function (CDF) of the raised cosine distribution.

The CDF of the raised cosine distribution is

\[F(x) = \frac{\pi + x + \sin(x)}{2\pi}\]

mpsci.distributions.cosine.invcdf(p)¶: Inverse of the CDF of the raised cosine distribution.

mpsci.distributions.cosine.invsf(p)¶: Inverse of the survival function of the cosine distribution.

mpsci.distributions.cosine.kurtosis()¶

Excess kurtosis of the cosine distribution.

The excess kurtosis is (6/5)*(90 - pi**4)/(pi**2 - 6)**2.

mpsci.distributions.cosine.logpdf(x)¶

Natual logarithm of the PDF of the raised cosine distribution.

The PDF of the raised cosine distribution is

\[f(x) = \frac{1 + \cos(x)}{2\pi}\]

on the interval \((-\pi, \pi)\) and zero elsewhere.

mpsci.distributions.cosine.mean()¶

Mean of the cosine distribution.

The mean is 0.

mpsci.distributions.cosine.pdf(x)¶

Probability density function (PDF) of the raised cosine distribution.

The PDF of the raised cosine distribution is

\[f(x) = \frac{1 + \cos(x)}{2\pi}\]

on the interval \((-\pi, \pi)\) and zero elsewhere.

mpsci.distributions.cosine.sf(x)¶: Survival function for the cosine distribution.

mpsci.distributions.cosine.skewness()¶

Skewness of the cosine distribution.

The skewness is 0.

mpsci.distributions.cosine.var()¶

Variance of the cosine distribution.

The variance is pi**2/3 - 2.