We provide numba-accelerated implementations of statistical functions for common probability distributions

• Uniform
• (Truncated) Normal
• Log-normal
• Poisson
• (Truncated) Exponential
• Student's t
• Voigtian
• Crystal Ball
• Generalised double-sided Crystal Ball
• Tsallis-Hagedorn, a model for the minimum bias pT distribution
• Q-Gaussian
• Bernstein density (not normalised to unity, use this in extended likelihood fits)

with more to come. The speed gains are huge, up to a factor of 100 compared to scipy. Benchmarks are included in the repository and are run by pytest.

Each distribution is implemented in a submodule. Import the submodule that you need.

from numba_stats import norm
import numpy as np

x = np.linspace(-10, 10)
mu = 2
sigma = 3

dp = norm.pdf(x, mu, sigma)
p = norm.cdf(x, mu, sigma)

The functions are vectorised on the variate x, but not on the shape parameters of the distribution. Ideally, the following functions are implemented for each distribution:

• logpdf
• pdf
• cdf
• ppf

cdf and ppf are missing for some distributions (e.g. voigt), if there is currently no fast implementation available. logpdf is only implemented if it is more efficient and accurate compared to computing log(dist.pdf(...)).

To get documentation, please use help() in the Python interpreter.

Functions with equivalents in scipy.stats follow the Scipy calling conventions exactly. These conventions are sometimes a bit unusual, for example, in case of the exponential, the log-normal or the uniform distribution. See the SciPy docs for details.

You can help with adding more distributions, patches are very welcome. Implementing a probability distribution is easy. You need to write it in simple Python that numba can understand. Special functions from scipy.special can be used after some wrapping, see submodule numba_stats._special.py how it is done.

numba-scipy is the official package and repository for fast numba-accelerated scipy functions, are we reinventing the wheel?

Ideally, the functionality in this package should be in numba-scipy and we hope that eventually this will be case. In this package, we don't offer overloads for scipy functions and classes like numba-scipy does. This simplifies the implementation dramatically. numba-stats is intended as a temporary solution until fast statistical functions are included in numba-scipy. numba-stats currently does not depend on numba-scipy, only on numba and scipy.