Distributions

Distribution families for Location, Scale, and Shape (LSS) regression. Each distribution defines a parametric family and methods for computing negative log-likelihood loss.

Overview

DeepTab’s LSS models can predict full probability distributions instead of point estimates. This is useful for uncertainty quantification, probabilistic forecasting, and heteroskedastic regression.

Available Distributions

Continuous Distributions

Distribution	Use Case
NormalDistribution	General continuous targets; default choice.
LogNormalDistribution	Strictly positive targets with multiplicative noise (prices, incomes).
StudentTDistribution	Robust to outliers; heavy-tailed data.
GammaDistribution	Positive continuous targets (durations, amounts).
InverseGammaDistribution	Positive targets with right skew.
BetaDistribution	Bounded targets in (0, 1) interval (proportions, rates).
JohnsonSuDistribution	Flexible shape; can model skewness and kurtosis.
TweedieDistribution	Zero-inflated positive targets (insurance claims, rainfall).

Discrete Distributions

Distribution	Use Case
PoissonDistribution	Count data (non-negative integers).
ZeroInflatedPoissonDistribution	Count data with excess zeros.
NegativeBinomialDistribution	Overdispersed count data.
CategoricalDistribution	Multiclass classification with uncertainty.

Multivariate / Compositional Distributions

Distribution	Use Case
DirichletDistribution	Compositional data (proportions that sum to 1).
MultinomialDistribution	Multi-category count targets.
MixtureOfGaussiansDistribution	Multimodal continuous targets (bimodal price distributions etc.).

Quantile Regression

Distribution	Use Case
Quantile	Predict arbitrary percentiles; distribution-free.

Quick Example

from deeptab.models import MambularLSS

# Fit a distributional model
model = MambularLSS()
model.fit(X_train, y_train, family="normal")

# Predict distribution parameters as an array of shape (n_samples, n_params).
# For the normal family the columns are (loc, scale).
params = model.predict(X_test)

# Score with distribution-aware metrics such as CRPS and NLL
scores = model.evaluate(X_test, y_test)

For worked examples that turn these parameters into prediction intervals and calibration plots, see the Uncertainty Quantification tutorial.

Choosing a Distribution

family=	Target type	Use when
"normal"	Continuous	Default starting point; symmetric noise around a mean.
"studentt"	Continuous	Outliers are present; need heavier tails than Normal.
"lognormal"	Positive continuous	Multiplicative noise; targets span multiple orders of magnitude (prices, incomes).
"gamma"	Positive continuous	Strictly positive targets with right skew (durations, rainfall amounts).
"inversegamma"	Positive continuous	Positive targets with a longer right tail than Gamma.
"beta"	(0, 1) bounded	Proportions, rates, probabilities that must stay in (0, 1).
"johnsonsu"	Continuous	Need to model both skewness and excess kurtosis simultaneously.
"tweedie"	Zero-inflated positive	Mix of exact zeros and positive values (insurance claims, rainfall).
"poisson"	Count	Non-negative integer counts with mean ≈ variance.
"zip"	Count	Count data with more zeros than Poisson predicts.
"negativebinom"	Count	Overdispersed counts (variance > mean).
"categorical"	Multiclass	Classification with calibrated class probabilities.
"dirichlet"	Compositional	Vectors of proportions that must sum to 1.
"multinomial"	Multi-category count	Integer-valued compositional targets.
"mog"	Continuous multimodal	Targets with multiple distinct peaks (mixture of regimes).
"quantile"	Distribution-free	Predict specific percentiles without assuming a parametric family.

See Also

• Uncertainty Quantification: Complete LSS examples

• deeptab.models.MambularLSS: LSS model reference

API Reference

• deeptab.distributions