Distribution Registry

nemora registers every probability density function (PDF) in the generalized beta family that was validated in the legacy workflows, together with the canonical Weibull and Gamma forms. All distributions are exposed through the registry functions in nemora.distributions and can be used interchangeably by the fitting workflows and CLI.

Parameter Conventions

• s denotes the scaling parameter introduced by the two-stage workflow. It is optional and only present when the underlying manuscript used a complete-form PDF with a free scale factor.

• a, b, p, q follow the notation from Ducey & Gove (2015) for the generalized beta families.

• beta represents the scale parameter of the generalized gamma specialisations.

• mu / sigma2 correspond to the log-scale mean and variance for the lognormal construction.

• u, v, d, df retain their classical meanings for the F, UG, and half-t distributions.

All parameters are strictly positive unless otherwise noted; the registry populates conservative starting values that can be overridden via FitConfig.

Registered Distributions

Name	Parameters	Description
weibull	a, beta, s	Complete-form Weibull distribution.
gamma	beta, p, s	Gamma distribution with free scaling factor.
gb1	a, b, p, q, s	Generalized beta distribution of the first kind (GB1).
gb2	a, b, p, q, s	Generalized beta distribution of the second kind (GB2).
gg	a, beta, p, s	Generalized gamma parent distribution.
ib1	b, p, q, s	Inverted beta type I (GB1 with a = -1).
ug	b, d, q, s	Upper generalized distribution limit of GB1.
b1	b, p, q, s	Classical beta distribution on (0, b).
b2	b, p, q, s	Beta distribution of the second kind.
sm	a, b, q, s	Singh–Maddala distribution.
dagum	a, b, p, s	Dagum (inverse Burr) distribution.
pareto	b, p, s	Pareto distribution.
p	b, p, s	Pearson type V distribution.
ln	mu, sigma2, s	Lognormal distribution derived from the generalized gamma limit.
ga	beta, p, s	Gamma distribution (alias to gamma without renaming parameters).
w	a, beta, s	Weibull distribution (alias to weibull).
f	u, v, s	Fisher–Snedecor F distribution.
l	b, q, s	Log-logistic (Type I) distribution.
il	b, p, s	Inverse log-logistic (Type II) distribution.
fisk	a, b, s	Fisk (log-logistic) distribution with explicit shape parameter.
u	b, s	Uniform distribution on (0, b).
halfn	sigma2, s	Half-normal distribution.
chisq	p, s	Chi-square distribution.
exp	beta, s	Exponential distribution.
r	beta, s	Rayleigh distribution.
halft	df, s	Half-Student t distribution.
ll	b, s	Log-logistic distribution with equal shape parameters.

.. todo:: Update this section once the nemora.ingest / sampling / synthesis modules land to reflect the broader workflow.