# arch.univariate.SkewStudent¶

class arch.univariate.SkewStudent(random_state=None, *, seed=None)[source]

Standardized Skewed Student’s distribution for use with ARCH models

Parameters
random_state : RandomState, optional

Deprecated since version 5.0: random_state is deprecated. Use seed instead.

seed : {int, Generator, RandomState}, optional

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

1

Hansen, B. E. (1994). Autoregressive conditional density estimation. International Economic Review, 35(3), 705–730. <https://www.ssc.wisc.edu/~bhansen/papers/ier_94.pdf>

Methods

 bounds(resids) Parameter bounds for use in optimization. cdf(resids[, parameters]) Cumulative distribution function 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 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 random_state The NumPy RandomState attached to the distribution