Example

Suppose we want to implement the expected value of log-normal distribution with location parameter \mu and scale parameter \sigma.

>>> import numpy as np
>>>
>>> def lognormal_expectation(mu, sigma):
...   return np.exp(mu + sigma ** 2 / 2)
>>>
>>> def lognormal_expectation_wrong(mu, sigma):
...   return np.exp(mu + sigma ** 2)

We can validate our implementation by simulating from a lognormal distribution and comparing with the bootstrapped mean.

>>> from pytest_bootstrap import bootstrap_test
>>>
>>> mu = -1
>>> sigma = 1
>>> reference = lognormal_expectation(mu, sigma)
>>> x = np.exp(np.random.normal(mu, sigma, 1000))
>>> result = bootstrap_test(x, np.mean, reference)

This returns a summary of the test, such as the bootstrapped statistics.

>>> result.keys()
dict_keys(['alpha', 'alpha_corrected', 'reference', 'lower', 'upper',
           'z_score', 'median', 'iqr', 'tol', 'statistics'])

Comparing with our incorrect implementation reveals the bug.

>>> reference_wrong = lognormal_expectation_wrong(mu, sigma)
>>> result = bootstrap_test(x, np.mean, reference_wrong)
Traceback (most recent call last):
  ...
pytest_bootstrap.BootstrapTestError: the reference value 1.0 lies outside
  the 1 - (alpha = 0.01) interval ...

Visualising the bootstrapped distribution using pytest_bootstrap.result_hist can help identify discrepancies between the bootstrapped statistics and the theoretical reference value. Note that you need to install matplotlib separately or install pytest-bootstrap using pip install pytest-bootstrap[plot].

.. plot:: examples/lognormal.py
:caption: Histogram of bootstrapped means reveals the erroneous implementation of the log-normal mean.

A comprehensive set of examples can be found in the tests.

Interface

.. automodule:: pytest_bootstrap
:members: