arch.univariate.Normal¶

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

Standard normal 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 normally distributed, 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