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

mvsk (list of mu, mc2, skew, kurt) – distribution is matched to these four moments

Returns

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

Return type

function

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

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