mixle.stats.univariate.continuous.logistic module

Create, estimate, and sample from a location-scale logistic distribution.

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

class LogisticDistribution(loc=0.0, scale=1.0, name=None, keys=None)

Bases: SequenceEncodableProbabilityDistribution

Logistic distribution with location loc and scale > 0.

Parameters:

• loc (float)

• scale (float)

• name (str | None)

• keys (str | None)

classmethod compute_capabilities()

classmethod compute_declaration()

static backend_legacy_sufficient_statistics(x, params, engine)

Return per-row Logistic sufficient statistics in accumulator order.

Parameters:

• x (Any)

• params (dict[str, Any])

• engine (Any)

Return type:

tuple[Any, …]

density(x)

Return the probability density or mass at a single observation.

Parameters:

x (float)

Return type:

float

log_density(x)

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

Parameters:

x (float)

Return type:

float

seq_log_density(x)

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

Parameters:

x (ndarray)

Return type:

ndarray

static backend_log_density_from_params(x, loc, scale, engine)

Engine-neutral logistic log-density from explicit parameters.

Parameters:

• x (Any)

• loc (Any)

• scale (Any)

• engine (Any)

Return type:

Any

backend_seq_log_density(x, engine)

Engine-neutral vectorized log-density for encoded data.

Parameters:

• x (Any)

• engine (Any)

Return type:

Any

classmethod backend_stacked_params(dists, engine)

Return stacked logistic parameters for a homogeneous mixture kernel.

Parameters:

• dists (Sequence[LogisticDistribution])

• engine (Any)

Return type:

dict[str, Any]

classmethod backend_stacked_log_density(x, params, engine)

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

Parameters:

• x (Any)

• params (dict[str, Any])

• engine (Any)

Return type:

Any

cdf(x)

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

Parameters:

x (float)

Return type:

float

quantile(q)

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

Parameters:

q (float)

Return type:

float

mean()

Mean E[X] of the distribution.

Return type:

float

variance()

Variance Var[X] of the distribution.

Return type:

float

entropy()

Differential entropy log(scale) + 2.

Return type:

float

skewness()

Skewness (0).

Return type:

float

kurtosis()

Excess kurtosis (6/5).

Return type:

float

mode()

Mode (= the location loc).

Return type:

float

sampler(seed=None)

Return a sampler for drawing observations from this distribution.

Parameters:

seed (int | None)

Return type:

LogisticSampler

estimator(pseudo_count=None)

Return an estimator for fitting this distribution from data.

Parameters:

pseudo_count (float | None)

Return type:

LogisticEstimator

dist_to_encoder()

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

Return type:

LogisticDataEncoder

class LogisticSampler(dist, seed=None)

Bases: DistributionSampler

Draw iid logistic observations.

Parameters:

• dist (LogisticDistribution)

• seed (int | None)

sample(size=None)

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 LogisticAccumulator(name=None, keys=None)

Bases: SequenceEncodableStatisticAccumulator

Accumulate weighted first and second moments for logistic estimation.

Parameters:

• name (str | None)

• keys (str | None)

update(x, weight, estimate)

Parameters:

• x (float)

• weight (float)

• estimate (LogisticDistribution | None)

Return type:

None

initialize(x, weight, rng)

Parameters:

• x (float)

• weight (float)

• rng (RandomState | None)

Return type:

None

seq_update(x, weights, estimate)

Parameters:

• x (ndarray)

• weights (ndarray)

• estimate (LogisticDistribution | None)

Return type:

None

seq_initialize(x, weights, rng)

Parameters:

• x (ndarray)

• weights (ndarray)

• rng (RandomState | None)

Return type:

None

combine(suff_stat)

Parameters:

suff_stat (tuple[float, float, float])

Return type:

LogisticAccumulator

value()

Return type:

tuple[float, float, float]

from_value(x)

Parameters:

x (tuple[float, float, float])

Return type:

LogisticAccumulator

key_merge(stats_dict)

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)

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()

Return type:

LogisticDataEncoder

class LogisticAccumulatorFactory(name=None, keys=None)

Bases: StatisticAccumulatorFactory

Factory for LogisticAccumulator.

Parameters:

• name (str | None)

• keys (str | None)

make()

Return type:

LogisticAccumulator

class LogisticEstimator(pseudo_count=None, suff_stat=None, min_scale=1.0e-8, name=None, keys=None)

Bases: ParameterEstimator

Moment estimator for logistic location and scale.

The likelihood MLE has no closed-form M-step. The EM estimator uses the identities mean=loc and var=pi^2 scale^2 / 3; torch gradient MLE can refine both parameters when exact likelihood optimization is desired.

Parameters:

• pseudo_count (float | None)

• suff_stat (tuple[float, float] | None)

• min_scale (float)

• name (str | None)

• keys (str | None)

accumulator_factory()

Return type:

LogisticAccumulatorFactory

estimate(nobs, suff_stat)

Parameters:

• nobs (float | None)

• suff_stat (tuple[float, float, float])

Return type:

LogisticDistribution

class LogisticDataEncoder

Bases: DataSequenceEncoder

Encode logistic observations as a float array.

seq_encode(x)

Encode the iid observation sequence x for vectorized evaluation.

Parameters:

x (Sequence[float])

Return type:

ndarray