statsmodels.sandbox.distributions.extras.NormExpan_gen

class statsmodels.sandbox.distributions.extras.NormExpan_gen(args, **kwds)

Gram-Charlier Expansion of Normal distribution

class follows scipy.stats.distributions pattern but with __init__

Notes

The distribution is defined as the Gram-Charlier expansion of the normal distribution using the first four moments. The pdf is given by

pdf(x) = (1+ skew/6.0 * H(xc,3) + kurt/24.0 * H(xc,4))*normpdf(xc)

where xc = (x-mu)/sig is the standardized value of the random variable and H(xc,3) and H(xc,4) are Hermite polynomials

Note: This distribution has to be parametrized during initialization and instantiation, and does not have a shape parameter after instantiation (similar to frozen distribution except for location and scale.) Location and scale can be used as with other distributions, however note, that they are relative to the initialized distribution.

Attributes:

random_state

Get or set the generator object for generating random variates.

Methods

__call__(*args, **kwds)

Freeze the distribution for the given arguments.

Methods

cdf(x, *args, **kwds)	Cumulative distribution function of the given RV.
entropy(*args, **kwds)	Differential entropy of the RV.
expect([func, args, loc, scale, lb, ub, ...])	Calculate expected value of a function with respect to the distribution by numerical integration.
fit(data, *args, **kwds)	Return estimates of shape (if applicable), location, and scale parameters from data.
fit_loc_scale(data, *args)	Estimate loc and scale parameters from data using 1st and 2nd moments.
freeze(*args, **kwds)	Freeze the distribution for the given arguments.
interval(alpha, *args, **kwds)	Confidence interval with equal areas around the median.
isf(q, *args, **kwds)	Inverse survival function (inverse of sf) at q of the given RV.
logcdf(x, *args, **kwds)	Log of the cumulative distribution function at x of the given RV.
logpdf(x, *args, **kwds)	Log of the probability density function at x of the given RV.
logsf(x, *args, **kwds)	Log of the survival function of the given RV.
mean(*args, **kwds)	Mean of the distribution.
median(*args, **kwds)	Median of the distribution.
moment(n, *args, **kwds)	n-th order non-central moment of distribution.
nnlf(theta, x)	Negative loglikelihood function.
pdf(x, *args, **kwds)	Probability density function at x of the given RV.
ppf(q, *args, **kwds)	Percent point function (inverse of cdf) at q of the given RV.
rvs(*args, **kwds)	Random variates of given type.
sf(x, *args, **kwds)	Survival function (1 - cdf) at x of the given RV.
stats(*args, **kwds)	Some statistics of the given RV.
std(*args, **kwds)	Standard deviation of the distribution.
support(*args, **kwargs)	Support of the distribution.
var(*args, **kwds)	Variance of the distribution.

Properties

random_state

Get or set the generator object for generating random variates.