arch.univariate.StudentsT

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

Standardized Student’s distribution for use with ARCH models

Parameters:
random_state: RandomState | None = None

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

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.

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) 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

random_state

The NumPy RandomState attached to the distribution