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