distsfactory

A Python package for constructing probability distributions from partial specifications — moments, quantiles, mode, and support.

Part of the DistributionsFactories family (alongside DistributionsFactories.jl for Julia and distsfactory-r). The Julia package is the parameterization master; this Python port mirrors its behaviour and is cross-validated against it.

Design

• Built on scipy.stats — returns frozen scipy distribution objects (or scipy-compatible wrappers) that work with the rest of the scientific Python ecosystem.
• Specify what you know (mean, variance, quantiles, mode, support) and get back a ready-to-use distribution.
• Accepts distribution names as strings or scipy.stats distribution objects directly.

Quick start

from distsfactory import make_dist

# Construct from moments — returns a frozen scipy.stats distribution
d = make_dist("gamma", mean=5, var=3)
type(d)            # scipy.stats._distn_infrastructure.rv_continuous_frozen

d.pdf(2)           # density
d.cdf(0.95)        # CDF
d.ppf(0.5)         # quantile (percent point function)
d.rvs(100)         # random samples
d.mean()           # 5.0
d.var()            # 3.0

# scipy.stats objects work too
import scipy.stats as st
d = make_dist(st.gamma, mean=5, var=3)

# Truncated Normal on [-1, 4] with mean 1 and standard deviation 0.8
d = make_dist("normal", mean=1.0, std=0.8, support=(-1, 4))
type(d)                    # scipy.stats._distn_infrastructure.rv_continuous_frozen
                           # (a scipy.stats.truncnorm)
d.mean(), d.std()          # (1.0, 0.8)  — moments after truncation
d.kwds                     # {'a': -2.408, 'b': 3.666,
                           #  'loc': 0.9822, 'scale': 0.8232}
                           # — parent Normal(μ, σ) solved so the truncated
                           #   distribution hits the requested (mean, std)

Whenever scipy provides a native truncated form (truncnorm, truncexpon, …) we return that. For families where scipy doesn't (Truncated{Laplace}, Truncated{Gamma}, …) the return is a distsfactory._support._TruncatedDist wrapper with the same pdf/cdf/ppf/mean/var/rvs surface.

Supported distributions

27 families across continuous (real, positive, unit) and discrete supports. Each family supports a subset of specification types — mean+var is universal; quantile- and mode-based forms are implemented where they exist in the Julia package.

Continuous on (-∞, ∞)

Continuous on [0, ∞)

Continuous on [0, 1]

Discrete

Specification styles

# Moment-based
make_dist("gamma", mean=5, var=3)
make_dist("gamma", mean=5, std=2)          # std -> var
make_dist("gamma", mean=5, cv=0.5)         # coefficient of variation
make_dist("gamma", mean=4, scv=0.5)        # squared CV
make_dist("gamma", mean=5, second_moment=28)  # E[X²] -> var
make_dist("exponential", mean=3)           # 1-parameter family

# Quantile-based
make_dist("exponential", median=2.0)
make_dist("logistic", q1=2, q3=8)
make_dist("normal", q1=-1, q3=1)
make_dist("gamma", quantiles=[(0.1, 1.0), (0.9, 10.0)])
make_dist("beta", mean=0.4, median=0.38)
make_dist("normal", median=5, iqr=2)

# Mode-based
make_dist("rayleigh", mode=2)
make_dist("gamma", mean=5, mode=3)
make_dist("beta", mean=0.4, mode=0.35)
make_dist("gamma", mode=3, iqr=4)
make_dist("normal", mode=3, var=4)
make_dist("logistic", mode=5, iqr=4)

# 3-parameter triangular (mean + var + mode)
make_dist("triangular", mean=5, var=2, mode=4)
make_dist("discrete_triangular", mean=5, var=2, mode=5)

Support — affine transforms and truncation

The support= keyword places a distribution on an arbitrary support. The package chooses between an affine transform (when the requested support has the same shape as the natural one) and truncation (when it's strictly contained).

import math

# Affine shift — Gamma on [3, ∞)
make_dist("gamma", mean=8, var=3, support=(3, math.inf))

# Affine flip — Gamma on (-∞, 10]
make_dist("gamma", mean=5, var=3, support=(-math.inf, 10))

# Affine scale — Beta on [2, 7]
make_dist("beta", mean=3.5, var=0.5, support=(2, 7))

# Truncation — Normal on [-0.5, 0.5] with moment matching (2D Newton)
make_dist("normal", mean=0.1, var=0.05, support=(-0.5, 0.5))

# Truncation — Gamma/Beta with actual moment matching (generic 2D Newton)
make_dist("gamma", mean=3, var=1, support=(0, 10))
make_dist("beta", mean=0.5, var=0.02, support=(0.2, 0.8))

# Discrete shift — Binomial on {10, …, 15}
make_dist("binomial", mean=12, var=1.2, support=range(10, 16))

# Truncated Poisson on {2, …, 10} (var is determined by mean)
make_dist("poisson", mean=2.5, var=0.59, support=range(2, 11))

For location-scale Student-t, use partial_dist together with support=:

from distsfactory import partial_dist, make_dist

spec = partial_dist("tdist", df=5)
# Half-truncated location-scale Student-t
d = make_dist(spec, mean=2.0, var=1.0, support=(0.0, math.inf))

(Two-sided Truncated{TDist} is not implemented yet — same gap as in the Julia package; see #2.)

Partial specifications — partial_dist

The Python analog of Julia's @dist macro. Pin some scipy parameters and leave the rest to be solved from moment constraints.

from distsfactory import partial_dist, make_dist

# Pin Gamma's shape, solve scale from mean
spec = partial_dist("gamma", a=3.0)
d = make_dist(spec, mean=5.0)
d.kwds                # {'a': 3.0, 'scale': 1.6666…}

# Pin Gamma's shape, solve scale from variance
d = make_dist(spec, var=3.0)

# Pin Logistic's location, solve scale from variance
spec = partial_dist("logistic", loc=2.0)
d = make_dist(spec, var=22.3)

# Pin Beta's α, solve β from mean
spec = partial_dist("beta", a=2.0)
d = make_dist(spec, mean=0.4)
d.kwds                # {'a': 2.0, 'b': 3.0}

# Full instance — Student-t with df=7, solve loc/scale from (mean, var)
spec = partial_dist("tdist", df=7)
d = make_dist(spec, mean=5.0, var=2.0)

partial_dist uses the canonical (Julia-compatible) parameter set for each family. For example, gamma exposes (a, scale) — not (a, loc, scale) — because Julia's Gamma has only (α, θ). To shift the support, use support=.

Feasibility checks

from distsfactory import dist_exists

dist_exists("beta", mean=0.5, var=0.1)         # True
dist_exists("beta", mean=0.5, var=0.3)         # False (var too large)
dist_exists("exponential", mean=2.5, var=6.25) # True (var == mean²)
dist_exists("exponential", mean=2.5, var=1.5)  # False
dist_exists("tdist", mean=1, var=2)            # False (TDist requires mean=0)

When make_dist fails for the same input, it raises ValueError carrying the same reason string.

Discovery

from distsfactory import available_distributions
import math

# All distributions feasible for these moments
available_distributions(mean=5, var=3)
# ['normal', 'laplace', 'logistic', 'gumbel', 'uniform', 'sym_triangular',
#  'gamma', 'erlang', 'lognormal', 'weibull', 'frechet', 'inverse_gamma',
#  'pareto', 'folded_normal']

# Filter by natural support: tuple, range, or category string
available_distributions(support="positive")
available_distributions(support=(0, math.inf), mean=5, var=3)
available_distributions(support=(0, 1), mean=0.5, var=0.05)  # -> ['beta']
available_distributions(support="integer_nonneg")

Testing

The test suite is self-contained — pytest covers the package end-to-end with no Julia install required.

One additional file, tests/test_cross_julia.py, reads a checked-in JSON oracle (tests/data/cross_oracle.json) of reference values generated by the Julia package. It catches any cross-language numerical drift. The oracle is produced by scripts/build_cross_oracle.jl in the Julia repo, which by default writes the oracle into both the Python and R sibling-package test directories in a single run. Regenerate after material changes with:

cd ../DistributionsFactories.jl
julia --project=. scripts/build_cross_oracle.jl

Installation

pip install distsfactory

Requires Python ≥ 3.10. Pulls in scipy >= 1.11 and numpy >= 1.24.

Development install:

pip install -e ".[dev]"

Releases are cut from a git tag; see PUBLISHING.md.

Known residuals (parity with Julia)

The Julia package is the parameterization master. Inherited issues are tracked locally with a link to the upstream Julia issue:

• #1 — Gamma from_mean_mode accepts negative mode (bug; mirrors Julia #7)
• #2 — two-sided Truncated{TDist} not implemented (mirrors Julia #1)
• #3 — parse_spec silently drops std when both var and std passed (mirrors Julia #10)
• #4 — Erlang is approximate but undocumented (mirrors Julia #11)
• #5 — Frechet single-point start at CV²==1 (mirrors Julia #12)

Authors

Ron Ashri, Sarat Moka, Yoni Nazarathy