polars-sdist 0.1.0

Statistical distributions as native Polars expressions — PDF, CDF, PPF, SF, and sampling for 20+ distributions, powered by Rust.

polars-sdist

Statistical distributions as native Polars expressions. Built with Rust and PyO3 for zero-copy, vectorized computation over Polars DataFrames.

Install

pip install polars-sdist

Quick start

import polars as pl
from polars_sdist import SdistNamespace as sdist

df = pl.DataFrame({"x": [-1.96, 0.0, 1.96]})

# CDF, PDF, PPF, SF, ln_pdf — all as expressions
df.with_columns(
    cdf=sdist(pl.col("x")).normal_cdf(mu=0, sigma=1),
    pdf=sdist(pl.col("x")).normal_pdf(mu=0, sigma=1),
    sf=sdist(pl.col("x")).normal_sf(mu=0, sigma=1),
)

Inverse CDF (PPF)

df = pl.DataFrame({"p": [0.025, 0.5, 0.975]})
df.with_columns(
    z=sdist(pl.col("p")).normal_ppf(mu=0, sigma=1),
)

Discrete distributions

df = pl.DataFrame({"k": [0, 1, 2, 3, 4, 5]}).cast({"k": pl.Float64})
df.with_columns(
    pmf=sdist(pl.col("k")).poisson_pmf(lambda_=3.0),
    cdf=sdist(pl.col("k")).poisson_cdf(lambda_=3.0),
)

Random sampling (fixed parameters)

import polars_sdist

s = polars_sdist.sample_normal(n=10_000, mu=0, sigma=1, seed=42)
s = polars_sdist.sample_beta(n=10_000, alpha=2, beta=5, seed=42)

Random sampling (column parameters)

df = pl.DataFrame({
    "mu": [0.0, 10.0, -10.0],
    "sigma": [1.0, 0.5, 2.0],
})
df.with_columns(
    sample=sdist(pl.col("mu")).sample_normal(sigma=pl.col("sigma"), seed=42),
)

Supported distributions

Continuous

Distribution	Parameters	PDF	CDF	PPF	SF	ln_pdf
Normal	mu, sigma	x	x	x	x	x
Log-Normal	mu, sigma	x	x	x	x	x
Beta	alpha, beta	x	x	x	x	x
Gamma	shape, rate	x	x	x	x	x
Exponential	lambda_	x	x	x	x	x
Cauchy	location, scale	x	x	x	x	x
Chi-Squared	df	x	x	x	x	x
Student's t	df	x	x	x	x	x
Fisher-Snedecor (F)	d1, d2	x	x	x	x	x
Gumbel	location, scale	x	x	x	x	x
Inverse Gamma	shape, scale	x	x	x	x	x
Laplace	location, scale	x	x	x	x	x
Pareto	shape, scale	x	x	x	x	x
Triangular	min, max, mode	x	x	x	x	x
Uniform	a, b	x	x	x	x	x
Weibull	shape, scale	x	x	x	x	x

Discrete

Distribution	Parameters	PMF	CDF	PPF	SF
Bernoulli	p	x	x	x	x
Binomial	n, p	x	x	x	x
Geometric	p	x	x	x	x
Hypergeometric	pop_size, success_states, draws	x	x	x	x
Negative Binomial	r, p	x	x	x	x
Poisson	lambda_	x	x	x	x
Discrete Uniform	a, b	x	x	x	x

Sampling-only

These distributions support random sampling but not PDF/CDF:

PERT, Skew-Normal, Inverse Gaussian, Frechet, Zeta, Zipf

Performance

Benchmarked end-to-end against scipy/numpy on 1M elements. Median of 5 runs after warmup.

Distribution	Operation	polars-sdist	scipy	Speedup
normal	pdf	8.6 ms	36.8 ms	4.3x
normal	ppf	20.9 ms	48.4 ms	2.3x
normal	sample	3.6 ms	7.6 ms	2.1x
normal	cdf	23.3 ms	37.2 ms	1.6x
lognormal	pdf	17.1 ms	63.8 ms	3.7x
lognormal	sample	7.2 ms	12.7 ms	1.8x
lognormal	ppf	27.8 ms	42.3 ms	1.5x
lognormal	cdf	32.5 ms	41.4 ms	1.3x
binomial	pmf	32.0 ms	86.2 ms	2.7x
binomial	sample	20.1 ms	30.5 ms	1.5x
chi-squared	sample	10.0 ms	16.7 ms	1.7x
chi-squared	pdf	49.2 ms	60.9 ms	1.2x
chi-squared	cdf	90.3 ms	110.9 ms	1.2x
beta	ppf	517.8 ms	601.1 ms	1.2x
beta	pdf	80.3 ms	89.5 ms	1.1x

polars-sdist is faster in 15 of 19 benchmarks. Areas where scipy is faster (beta CDF/sample, chi-squared PPF, binomial CDF) use highly optimized C/Fortran special-function implementations.

Run it yourself:

pip install scipy
python benchmarks/bench_distributions.py --sizes 1000000

License

MIT