statsmodels.sandbox.distributions.extras.pdf_mvsk¶

statsmodels.sandbox.distributions.extras.pdf_mvsk(mvsk)[source]¶

Return the Gaussian expanded pdf function given the list of 1st, 2nd moment and skew and Fisher (excess) kurtosis.

Parameters:¶

mvsklist of mu, mc2, skew, kurt

distribution is matched to these four moments

Returns:¶

pdffuncfunction

function that evaluates the pdf(x), where x is the non-standardized random variable.

Notes

Changed so it works only if four arguments are given. Uses explicit formula, not loop.

This implements a Gram-Charlier expansion of the normal distribution where the first 2 moments coincide with those of the normal distribution but skew and kurtosis can deviate from it.

In the Gram-Charlier distribution it is possible that the density becomes negative. This is the case when the deviation from the normal distribution is too large.

References

https://en.wikipedia.org/wiki/Edgeworth_series Johnson N.L., S. Kotz, N. Balakrishnan: Continuous Univariate Distributions, Volume 1, 2nd ed., p.30