Distributions

ngboost-lightning supports 12 probability distributions spanning regression, classification, count data, and survival analysis. Every distribution uses unconstrained internal parameterization (log-link or logit) so boosted tree predictions can take any real value.

Distribution Table

Distribution	Class	Parameters	CRPS	Use Case
Normal	Normal	mean, log_scale	Yes	General regression (default)
Log-Normal	LogNormal	mu, log_sigma	Yes	Positive, right-skewed targets
Exponential	Exponential	log_rate	Yes	Positive targets, waiting times
Gamma	Gamma	log_alpha, log_beta	Yes	Positive targets (non-diagonal Fisher)
Poisson	Poisson	log_rate	Yes	Count data
Laplace	Laplace	loc, log_scale	Yes	Heavy-tailed, robust regression
Student's T	StudentT	loc, log_scale, log_df	No	Heavy tails with learnable degrees of freedom
Weibull	Weibull	log_scale, log_concentration	No	Survival / time-to-event data
Half-Normal	HalfNormal	log_scale	No	Positive targets, folded normal
Cauchy	Cauchy	loc, log_scale	No	Extreme outliers
Bernoulli	Bernoulli	logit	No	Binary classification (default)
Categorical	k_categorical(K)	K-1 logits	No	Multiclass classification

The CRPS column indicates whether the distribution supports training with CRPScore. Distributions without CRPS support can only use LogScore (negative log-likelihood).

Choosing a Distribution

Continuous regression:

• Start with Normal — it works well for most problems.
• Use LogNormal if targets are strictly positive and right-skewed (e.g. prices, durations).
• Use Laplace if you want robustness to outliers (heavier tails than Normal, L1-like loss).
• Use StudentT for heavy tails with an automatically learned tail weight (3 parameters).
• Use Cauchy only for extreme outlier scenarios — the mean is undefined.

Positive targets:

• Exponential for simple rate modeling (1 parameter).
• Gamma for more flexible positive-valued modeling (2 parameters, non-diagonal Fisher).
• HalfNormal for positive targets that are concentrated near zero.

Count data:

• Poisson for non-negative integer targets.

Classification:

• Bernoulli for binary (used automatically by LightningBoostClassifier).
• k_categorical(K) for multiclass — you must specify K explicitly.

Survival:

• Weibull is the primary choice for time-to-event data with LightningBoostSurvival.
• LogNormal and Exponential also support logsf for survival modeling.

Using a Distribution

Pass the distribution class (not an instance) to the estimator:

from ngboost_lightning import LightningBoostRegressor, Laplace

reg = LightningBoostRegressor(dist=Laplace, n_estimators=200)
reg.fit(X_train, y_train)

dist = reg.pred_dist(X_test)
dist.mean()   # location parameter
dist.scale    # scale parameter

Fixed Degrees of Freedom (Student's T)

StudentT learns the degrees of freedom from data. If you want to fix it:

from ngboost_lightning import LightningBoostRegressor, t_fixed_df

reg = LightningBoostRegressor(dist=t_fixed_df(5), n_estimators=200)

StudentT3 is a convenience alias for t_fixed_df(3).

Distribution Interface

All distributions provide these methods after fitting:

Method	Description
mean()	Conditional mean
sample(n)	Random samples
cdf(y)	Cumulative distribution function
ppf(q)	Quantile function (inverse CDF)
logpdf(y)	Log probability density / mass
score(y)	Per-sample negative log-likelihood
logsf(y)	Log survival function (if supported)

See the API Reference for the complete Distribution abstract base class.