Bootstrap confidence interval estimation routines for Numpy/Scipy/Pandas

numpy, python, statistics
pip install scikits.bootstrap==1.1.0


DOI Codecov PyPI GitHub release (latest SemVer) PyPI - Python Version

Documentation: Stable, Latest.


Scikits.bootstrap provides bootstrap statistics confidence interval algorithms for Numpy/Scipy/Pandas. It originally required scipy, but no longer needs it.

It also provides an algorithm which estimates the probability that the statistics lies satisfies some criteria, e.g., lies in some interval.

Much of the code has been written based off the descriptions from Efron and Tibshirani's Introduction to the Bootstrap, and results should match the results obtained from following those explanations. However, the current ABC code is based off of the modified-BSD-licensed R port of the Efron bootstrap code, as I do not believe I currently have a sufficient understanding of the ABC method to write the code independently.

Please contact me (Constantine Evans, or Matrix <>) with any questions, suggestions, vulnerabilities, or other comments (PGP key), or, preferably, use Github's issue and pull requests.

If you'd like to add something, or make improvements, please keep the following in mind:

  • I'd like to keep the library as widely supported as possible, with as few dependencies as possible, preferably small ones. I'm also very wary of anything that would break backwards compatibility, even in unknown ways.

  • I am following semantic versioning.

  • Code should be black-formatted, and should have type annotations that work in 3.7 through the latest stable Python, and PyPy3.

  • Docstrings should be in Numpy format. They should preferably include references for the implemented algorithms (see the current code for examples).

  • All code should have working unit tests, preferably ones that do more than just testing fixed output with a fixed random seed, though given the non-deterministic nature of the bootstrap, good, deterministic tests may be difficult. Non-deterministic tests with extremely small chances of failure are acceptable, but shouldn't use such large numbers of samples that they overly slow down the tests.

  • I am a physicist, and am not very familiar with applications of the bootstrap for business or development statistics. So if you'd like to add something for those, it would be useful to give some more explanation than otherwise as to how they are generally useful.

The package is licensed under the BSD 3-Clause License. It is supported by the Evans Foundation.

Version Information

  • v1.1.0: Randomness is now generated via a numpy.random Generator. Anything that relied on using numpy.random.seed to obtain deterministic results will fail (mostly of relevance for testing). Seeds (or Generators) can now be passed to relevant functions with the seed argument, but note that changes in Numpy's random number generation means this will not give the same results that would be obtained using numpy.random.seed to set the seed in previous versions.

    There is a new pval function, and there are several bugfixes.

    Numba is now supported in some instances (np.average or np.mean as statfunction, 1-D data), using use_numba=True. Pypy3 is also supported. Typing information has been added, with code passing mypy --strict --allow-untyped-calls --ignore-missing-imports, and tests cover 100% of the code (though many tests use fixed seeds).

    Handling of multiple data sets (tuples/etc of arrays) now can be specified as multi="paired" (the previous handling), where the sets must be of the same length, and samples are taken keeping corresponding points connected, or multi="independent", treating data sets as independent and sampling them seperately (in which case they may be different sizes).

  • v1.0.1: Licensing information added.

  • v1.0.0: scikits.bootstrap now uses pyerf, which means that it doesn't actually need scipy at all. It should work with PyPy, has some improved error and warning messages, and should be a bit faster in many cases. The old ci_abc function has been removed: use method='abc' instead.

  • v0.3.3: Bug fixes. Warnings have been cleaned up, and are implemented for BCa when all statistic values are equal (a common confusion in prior versions). Related numpy warnings are now suppressed. Some tests on Python 2 were fixed, and the PyPI website link is now correct.

  • v0.3.2: This version contains various fixes to allow compatibility with Python 3.3. While I have not used the package extensively with Python 3, all tests now pass, and importing works properly. The compatibility changes slightly modify the output of bootstrap_indexes, from a Python list to a Numpy array that can be iterated over in the same manner. This should only be important in extremely unusual situations.

Installation and Usage

scikits.bootstrap is tested on Python 3.7 - 3.10, and PyPy 3. The package can be installed using pip.

pip install scikits.bootstrap

Usage example for python 3.x:

import scikits.bootstrap as boot
import numpy as np, np.average)