# Licensed under a 3-clause BSD style license - see LICENSE.rst
import numpy as np
__all__ = ["exptest"]
[docs]def exptest(time_delta):
"""Compute the level of variability for a certain period of time.
The level of variability is quantified by ``mr``, as defined in Prahl (1999).
For constant rate events, it follows a standard normal distribution,
i.e. it can be used directly as the significance of variability.
For example usage, see :ref:`time-variability`.
Parameters
----------
time_delta : array-like
Time differences between consecutive events
Returns
-------
mr : float
Level of variability
References
----------
.. [1] Prahl (1999), "A fast unbinned test on event clustering in Poisson processes",
`Link <https://ui.adsabs.harvard.edu/abs/1999astro.ph..9399P>`_
"""
mean_time = np.mean(time_delta)
normalized_time_delta = time_delta / mean_time
mask = normalized_time_delta < 1
sum_time = 1 - normalized_time_delta[mask] / 1
sum_time_all = np.sum([sum_time])
m_value = sum_time_all / len(time_delta)
# the numbers are from Prahl(1999), derived from simulations
term1 = m_value - (1 / 2.71828 - 0.189 / len(time_delta))
term2 = 0.2427 / np.sqrt(len(time_delta))
mr = term1 / term2
return mr