bartz.testing.DiscreteUniform

class bartz.testing.DiscreteUniform(m)[source]

Uniform distribution on m equispaced levels, standardized.

m=2 gives random signs (levels -1 and 1), whose squares are constant (kurtosis 1).

m: Integer[Array, ''] | int

Number of levels, >= 2.

property kurtosis: Float[Array, ''] | float[source]

Fourth moment E[z ** 4] = 3/5 (3m^2 - 7)/(m^2 - 1).

1 at m=2, increasing towards 9/5 (the continuous Uniform) as m grows.

sample(key, shape)[source]

Sample i.i.d. standardized values on the m levels.

Return type:

Float[Array, '*shape']

quantize(x, max_bins)[source]

Recover the levels, merged evenly if there are more than max_bins.

Parameters:

  • x (Float[Array, '*shape']) – Values drawn from the distribution, of any shape.

  • max_bins (int) – Maximum number of levels.

Returns:

  • quantized_x (UInt[Array, ‘*shape’]) – The bin indices, in [0, m).

  • m (Integer[Array, ‘’]) – The number of levels, min(self.m, max_bins).

ppf(u)[source]

Quantile function: map probabilities in [0, 1] to the m standardized levels.

Return type:

Float[Array, '*shape']

from_standard_normal(z)[source]

Map standard-Normal draws to this family, preserving their Gaussian copula.

Elementwise ppf(Phi(z)): each output is marginally a draw from this family (mean 0, variance 1) while the joint dependence of z carries over as a Gaussian copula. Normal overrides this with the identity.

Return type:

Float[Array, '*shape']