mousestyles.distributions package

Submodules

mousestyles.distributions.kolmogorov_test module

mousestyles.distributions.kolmogorov_test.get_travel_distances(strain=0, mouse=0, day=0)[source]

Get distances travelled in 20ms for this strain, this mouse, on this day.

Parameters:
  • strain (int {0, 1, 2}) – The strain of mouse to test
  • mouse (int {0, 1, 2, 3}) – The mouse twin id with in the strain
  • day (int {0, 1, ..., 11}) – The day to calculate the distance
Returns:

  • x (np.ndarray shape (n, 1)) – The distances travelled in 20ms for this mouse on this day, truncated at 1cm (i.e. only record mouse movement when it moves more than 1cm)
  • Examples
  • >>> get_travel_distances(0, 0, 0)[ (3])
  • array([ 1.00648944, 1.02094319, 1.0178885 ])
mousestyles.distributions.kolmogorov_test.perform_kstest(x, distribution=<scipy.stats._continuous_distns.pareto_gen object>, verbose=True)[source]

This function fits a distribution to data, and then test the fit of the distribution using Kolmogorov-Smirnov test.

The Kolmogorov-Smirnov test constructs the test statistic, which is defined as \(\sup |F_n(x) - F(x)|\), for \(F_n\) is the sample CDF, and F is the theoretical CDF. This statistics can be considered as a measure of distance between the sample distribution and the theoretical distribution. The smaller it is, the more similar the two distributions.

We first estimate the parameter using MLE, then by minimizing the KS test statistic.

The Pareto distribution is sometimes known as the Power Law distribution, with the PDF: \(b / x**(b + 1)\) for \(x >= 1, b > 0\). The truncated exponential distribution is the same as the rescaled exponential distribution.

Parameters:
  • x (np.ndarray (n,)) – The sample data to test the distribution
  • distribution (A Scipy Stats Continuous Distribution) – {stats.pareto, stats.expon, stats.gamma} The distribution to test against. Currently support pareto, expon, and gamma, but any one-sided continuous distribution in Scipy.stats should work.
  • verbose (boolean) – If True, will print out testing result
Returns:

  • params (np.ndarray shape (p,)) – The optimal parameter for the distribution. Optimal in the sense of minimizing K-S statistics.

  • The function also print out the Kolmogorov-Smirnov test result for three

  • cases

  • 1. When comparing the empirical distribution against the distribution with

  • parameters estimated with MLE

  • 2. When comparing the empirical distribution against the distribution with

  • parameters estimated by explicitely minimizing KS statistics

  • 3. When comparing a resample with replacement of the empirical distribution

  • against the Pareto in 2.

  • A p-value > 0.05 means we fail to reject the Null hypothesis that the

  • empirical distribution follow the specified distribution.

  • Notes

  • ——

  • The MLE often does not fit the data very well. We instead minimizing the

  • K-S distance, and obtain a better fit (as seen by the PDF and CDF

  • similarity between sample data and the fit)

  • References

  • ———– –

    1. Kolmogorov-Smirnov test:

      https://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test

    2. Pareto Distribution (also known as power law distribution)

      https://en.wikipedia.org/wiki/Pareto_distribution

  • Examples

  • ———

  • >>> x = get_travel_distances(0, 0, 0)

  • >>> res = perform_kstest(x, verbose=False)

  • >>> np.allclose(res, np.array([3.67593246, 0.62795748, 0.37224205]))

  • True

Module contents