mixle.stats.univariate.continuous.uniform module

Continuous uniform distributions over bounded intervals.

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

class UniformDistribution(low, high, name=None, keys=None)[source]

Bases: SequenceEncodableProbabilityDistribution

Continuous uniform distribution on [low, high].

Parameters:
classmethod compute_capabilities()[source]

Describe backend support for generated uniform kernels.

classmethod compute_declaration()[source]

Return the structured compute declaration for uniform distributions.

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 (ndarray)

Return type:

ndarray

static backend_log_density_from_params(x, low, high, engine)[source]

Engine-neutral uniform 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 uniform 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 uniform log densities.

Parameters:
Return type:

Any

classmethod backend_stacked_sufficient_statistics(x, weights, params, engine)[source]

Return stacked Uniform sufficient statistics using engine-resident arrays.

Parameters:
Return type:

tuple[Any, Any, 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 E[X] of the distribution.

Return type:

float

variance()[source]

Variance Var[X] of the distribution.

Return type:

float

entropy()[source]

Differential entropy log(high - low).

Return type:

float

skewness()[source]

Skewness (0).

Return type:

float

kurtosis()[source]

Excess kurtosis (-6/5).

Return type:

float

sampler(seed=None)[source]

Return a sampler for drawing observations from this distribution.

Parameters:

seed (int | None)

Return type:

UniformSampler

estimator(pseudo_count=None)[source]

Return an estimator for fitting this distribution from data.

Parameters:

pseudo_count (float | None)

Return type:

UniformEstimator

dist_to_encoder()[source]

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

Return type:

UniformDataEncoder

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

Bases: DistributionSampler

Draw iid uniform observations.

Parameters:

  • dist (UniformDistribution)

  • 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 UniformAccumulator(name=None, keys=None)[source]

Bases: SequenceEncodableStatisticAccumulator

Accumulate weighted min/max support statistics.

Parameters:

  • name (str | None)

  • keys (str | None)

update(x, weight, estimate)[source]

Accumulate support bounds and count from one weighted observation.

Parameters:

  • x (float)

  • weight (float)

  • estimate (UniformDistribution | 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 support bounds and count from encoded observations.

Parameters:
Return type:

None

seq_update_engine(x, weights, estimate, engine)[source]

Engine-resident accumulation of the weighted count (numpy or torch).

The support min/max are host scalar bookkeeping over the observed values.

Parameters:

  • x (ndarray)

  • weights (Any)

  • estimate (UniformDistribution | None)

  • engine (Any)

Return type:

None

seq_initialize(x, weights, rng)[source]

Initialize statistics from encoded observations.

Parameters:
Return type:

None

combine(suff_stat)[source]

Merge another uniform sufficient-statistic tuple.

Parameters:

suff_stat (tuple[float, float, float])

Return type:

UniformAccumulator

value()[source]

Return count and observed support bounds.

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:

UniformAccumulator

scale(c)[source]

Scale observation count while preserving support bounds.

Parameters:

c (float)

Return type:

UniformAccumulator

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:

UniformDataEncoder

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

Bases: StatisticAccumulatorFactory

Factory for UniformAccumulator.

Parameters:

  • name (str | None)

  • keys (str | None)

make()[source]

Create a fresh uniform accumulator.

Return type:

UniformAccumulator

class UniformEstimator(pseudo_count=None, suff_stat=None, min_width=1.0e-8, name=None, keys=None)[source]

Bases: ParameterEstimator

MLE estimator for uniform support endpoints.

Parameters:
accumulator_factory()[source]

Return an accumulator factory for uniform support statistics.

Return type:

UniformAccumulatorFactory

estimate(nobs, suff_stat)[source]

Estimate support endpoints from observed weighted bounds.

Parameters:
Return type:

UniformDistribution

class UniformDataEncoder[source]

Bases: DataSequenceEncoder

Encode uniform observations as a float array.

seq_encode(x)[source]

Encode observations as a floating-point array.

Parameters:

x (Sequence[float])

Return type:

ndarray