arch.univariate.SkewStudent¶

class arch.univariate.SkewStudent(*, seed: None | int | RandomState | Generator = None)[source]¶

Standardized Skewed Student’s distribution for use with ARCH models

Parameters:¶

seed: None | int | RandomState | Generator = None¶

Random number generator instance or int to use. Set to ensure reproducibility. If using an int, the argument is passed to np.random.default_rng. If not provided, default_rng is used with system-provided entropy.

Notes

The Standardized Skewed Student’s distribution ([1]) takes two parameters, \(\eta\) and \(\lambda\). \(\eta\) controls the tail shape and is similar to the shape parameter in a Standardized Student’s t. \(\lambda\) controls the skewness. When \(\lambda=0\) the distribution is identical to a standardized Student’s t.

References

Methods

bounds(resids)	Parameter bounds for use in optimization.
cdf(resids[, parameters])	Cumulative distribution function
constraints()	Construct arrays to use in constrained optimization.
loglikelihood(parameters, resids, sigma2[, ...])	Computes the log-likelihood of assuming residuals are have a standardized (to have unit variance) Skew Student's t distribution, conditional on the variance.
moment(n[, parameters])	Moment of order n
parameter_names()	Names of distribution shape parameters
partial_moment(n[, z, parameters])	Order n lower partial moment from -inf to z
ppf(pits[, parameters])	Inverse cumulative density function (ICDF)
simulate(parameters)	Simulates i.i.d.
starting_values(std_resid)	Construct starting values for use in optimization.

Properties

generator	The NumPy Generator or RandomState attached to the distribution
name	The name of the distribution