mixle.stats.univariate.continuous.uniform module

Create, estimate, and sample from a continuous uniform distribution.

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]
classmethod compute_declaration()[source]
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 observations.

Combinator samplers (mixture/sequence/…) accept batched. With batched=True (the default) each child stream is drawn in one vectorized call instead of a per-draw Python loop – far faster. Because every child sampler owns an independent RandomState, batching consumes each stream in the same order as the loop, so the draws are identical to the legacy path. batched=False forces that legacy per-draw loop as a guaranteed- stable reference. Leaf samplers are already vectorized and ignore the flag.

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]
Parameters:

  • x (float)

  • weight (float)

  • estimate (UniformDistribution | None)

Return type:

None

initialize(x, weight, rng)[source]
Parameters:
Return type:

None

seq_update(x, weights, estimate)[source]
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]
Parameters:
Return type:

None

combine(suff_stat)[source]
Parameters:

suff_stat (tuple[float, float, float])

Return type:

UniformAccumulator

value()[source]
Return type:

tuple[float, float, float]

from_value(x)[source]
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]

Pool this accumulator’s statistics into stats_dict under its merge key.

The structural default implements the common single-key pattern: store the accumulator under self.keys the first time the key is seen, else combine into the one already there. Accumulators with several named keys (e.g. an HMM’s init/trans/state keys) or a non-accumulator stats payload override this. A keys of None (the default) is a no-op.

Parameters:

stats_dict (dict[str, Any])

Return type:

None

key_replace(stats_dict)[source]

Replace this accumulator’s statistics from the pooled stats_dict entry (see key_merge).

Parameters:

stats_dict (dict[str, Any])

Return type:

None

acc_to_encoder()[source]
Return type:

UniformDataEncoder

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

Bases: StatisticAccumulatorFactory

Factory for UniformAccumulator.

Parameters:

  • name (str | None)

  • keys (str | None)

make()[source]
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 type:

UniformAccumulatorFactory

estimate(nobs, suff_stat)[source]
Parameters:
Return type:

UniformDistribution

class UniformDataEncoder[source]

Bases: DataSequenceEncoder

Encode uniform observations as a float array.

seq_encode(x)[source]

Encode the iid observation sequence x for vectorized evaluation.

Parameters:

x (Sequence[float])

Return type:

ndarray