fcaz.stats.Mixture

class fcaz.stats.Mixture(dists: Sequence[FrozenDistribution], weights: float | floating[Any] | NDArray[number[Any]] | Sequence[float | floating[Any] | NDArray[number[Any]]])

Finite mixture of frozen distributions (i.e., those with parameters already fixed).

Parameters:

• dists (sequence of frozen distributions) – Component distributions, e.g. scipy.stats.expon(scale=8).

• weights (array_like) – Non-negative mixing weights, one per component, summing to 1.

Raises:

ValueError – If dists and weights differ in length, or the weights are negative or do not sum to 1.

Notes

The survival function is \(S(x) = \sum_i w_i S_i(x)\); pdf, cdf and mean mix in the same way. hf and chf are derived from the mixed pdf and sf.

Examples

A 40% exponential, 60% inverse exponential mixture:

>>> from scipy import stats
>>> from fcaz.stats import invexpon, Mixture
>>> X = Mixture([stats.expon(scale=8), invexpon(scale=3)], [0.4, 0.6])
>>> round(float(X.chf(2.5)), 4)
0.3398

__init__(dists: Sequence[FrozenDistribution], weights: float | floating[Any] | NDArray[number[Any]] | Sequence[float | floating[Any] | NDArray[number[Any]]]) → None

Methods

__init__(dists, weights)
cdf(x)	Cumulative distribution function.
chf(x)	Cumulative hazard function, -log sf.
hf(x)	Hazard function, pdf / sf.
logsf(x)	Log of the survival function.
mean()	Mean of the mixture, the weighted mean of the component means.
pdf(x)	Probability density function.
ppf(q)	Percent point function (inverse cdf), solved numerically.
rvs([size, random_state])	Random variates; size and random_state as in scipy.
sf(x)	Survival function, 1 - cdf.