mixle.stats.univariate.continuous.weibull module

Two-parameter Weibull distributions over positive real values.

Reference: Johnson, Kotz & Balakrishnan, Continuous Univariate Distributions (2nd ed., Wiley, 1994/95).

class WeibullDistribution(shape, scale, name=None, keys=None)[source]

Bases: SequenceEncodableProbabilityDistribution

Weibull distribution with shape > 0 and scale > 0 on x >= 0.

Parameters:
classmethod compute_capabilities()[source]

Describe backend support for generated Weibull kernels.

classmethod compute_declaration()[source]

Return the structured compute declaration for Weibull distributions.

static backend_legacy_sufficient_statistics(x, params, engine)[source]

Return per-row Weibull sufficient statistics in accumulator order.

Parameters:
Return type:

tuple[Any, …]

density(x)[source]

Return the probability density or mass at a single observation.

Parameters:

x (float)

Return type:

float

log_density(x)[source]

Return the log-density or log-mass at a single observation.

Parameters:

x (float)

Return type:

float

seq_log_density(x)[source]

Return vectorized log-density values for sequence-encoded observations.

Parameters:

x (tuple[ndarray, ndarray])

Return type:

ndarray

static backend_log_density_from_params(vals, log_vals, shape, scale, engine)[source]

Engine-neutral Weibull log-density from explicit parameters.

Parameters:
Return type:

Any

backend_seq_log_density(x, engine)[source]

Engine-neutral vectorized log-density for encoded data.

Parameters:
Return type:

Any

classmethod backend_stacked_params(dists, engine)[source]

Return stacked Weibull parameters for a homogeneous mixture kernel.

Parameters:
Return type:

dict[str, Any]

classmethod backend_stacked_log_density(x, params, engine)[source]

Return an (n, k) matrix of Weibull log densities.

Parameters:
Return type:

Any

cdf(x)[source]

Cumulative distribution function P(X <= x) (exact). The continuous ‘index of’ a value.

Parameters:

x (float)

Return type:

float

quantile(q)[source]

Inverse CDF F^{-1}(q): the value at cumulative-probability index q (continuous unranking).

Parameters:

q (float)

Return type:

float

mean()[source]

Mean scale * Gamma(1 + 1/shape).

Return type:

float

variance()[source]

Variance scale^2 * (Gamma(1+2/shape) - Gamma(1+1/shape)^2).

Return type:

float

entropy()[source]

Differential entropy gamma*(1 - 1/shape) + log(scale/shape) + 1.

Return type:

float

mode()[source]

Mode scale*((k-1)/k)^(1/k) for shape k>1, else 0.

Return type:

float

sampler(seed=None)[source]

Return a sampler for drawing observations from this distribution.

Parameters:

seed (int | None)

Return type:

WeibullSampler

estimator(pseudo_count=None)[source]

Return an estimator for fitting this distribution from data.

Parameters:

pseudo_count (float | None)

Return type:

WeibullEstimator

dist_to_encoder()[source]

Return the data encoder used by this distribution for vectorized methods.

Return type:

WeibullDataEncoder

class WeibullSampler(dist, seed=None)[source]

Bases: DistributionSampler

Draw iid Weibull observations.

Parameters:

  • dist (WeibullDistribution)

  • seed (int | None)

sample(size=None)[source]

Draw one sample or an array of iid samples.

Parameters:

size (int | None)

Return type:

float | ndarray

class WeibullAccumulator(name=None, keys=None)[source]

Bases: SequenceEncodableStatisticAccumulator

Accumulate weighted first and second moments for Weibull estimation.

Parameters:

  • name (str | None)

  • keys (str | None)

update(x, weight, estimate)[source]

Accumulate weighted first and second moments for one observation.

Parameters:

  • x (float)

  • weight (float)

  • estimate (WeibullDistribution | None)

Return type:

None

initialize(x, weight, rng)[source]

Initialize statistics from one observation.

Parameters:
Return type:

None

seq_update(x, weights, estimate)[source]

Accumulate weighted first and second moments from encoded data.

Parameters:
Return type:

None

seq_initialize(x, weights, rng)[source]

Initialize statistics from encoded observations.

Parameters:
Return type:

None

combine(suff_stat)[source]

Merge another Weibull sufficient-statistic tuple.

Parameters:

suff_stat (tuple[float, float, float])

Return type:

WeibullAccumulator

value()[source]

Return accumulated sum, second moment sum, and count.

Return type:

tuple[float, float, float]

from_value(x)[source]

Replace accumulator contents from a sufficient-statistic tuple.

Parameters:

x (tuple[float, float, float])

Return type:

WeibullAccumulator

key_merge(stats_dict)[source]

Merge keyed statistics into stats_dict when keys are configured.

Parameters:

stats_dict (dict[str, Any])

Return type:

None

key_replace(stats_dict)[source]

Replace this accumulator from keyed statistics when available.

Parameters:

stats_dict (dict[str, Any])

Return type:

None

acc_to_encoder()[source]

Return the encoder used by this accumulator.

Return type:

WeibullDataEncoder

class WeibullAccumulatorFactory(name=None, keys=None)[source]

Bases: StatisticAccumulatorFactory

Factory for WeibullAccumulator.

Parameters:

  • name (str | None)

  • keys (str | None)

make()[source]

Create a fresh Weibull accumulator.

Return type:

WeibullAccumulator

class WeibullEstimator(pseudo_count=None, suff_stat=None, min_shape=1.0e-3, max_shape=1.0e3, min_scale=1.0e-12, name=None, keys=None)[source]

Bases: ParameterEstimator

Moment estimator for Weibull shape and scale.

Parameters:
accumulator_factory()[source]

Return an accumulator factory for Weibull moment statistics.

Return type:

WeibullAccumulatorFactory

estimate(nobs, suff_stat)[source]

Estimate shape and scale by matching weighted moments.

Parameters:
Return type:

WeibullDistribution

class WeibullDataEncoder[source]

Bases: DataSequenceEncoder

Encode Weibull observations with x and log(x).

seq_encode(x)[source]

Encode observations as values and log-values.

Parameters:

x (Sequence[float])

Return type:

tuple[ndarray, ndarray]