* Kolmogorov-Smirnov distribution #421
Add a new distribution, kolmogorov_smirnov_distribution, which takes a
parameter that represents the number of observations used in a
Kolmogorov-Smirnov test. (The K-S test is a popular test for comparing
two CDFs, but the test statistic is not implemented here.)
This implementation includes Kolmogorov's original 1st order Taylor
expansion. There is a literature on the distribution's other
mathematical properties (higher order terms and exact version); this
literature is summarized in the main header file for anyone who may
want to expand the implementation later.
The CDF is implemented using a Jacobi theta function, and the PDF is a
hand-rolled derivative of that function. Quantiles plug the CDF and PDF
into a Newton-Raphson iteration. The mean and variance have nice
closed-form expressions, and the mode uses a dumb run-time maximizer.
This commit includes graphs, a ULP plotter for the PDF, and the usual
compilation and numerical tests. The test file is on the small side, but
it integrates the distribution from zero to infinity, and covers the
quantiles pretty well. As of now the numerical tests only verify
self-consistency (e.g. distribution moments and CDF-quantile relations),
so there's room to add some external checks.
* Implement skewness for K-S distribution [CI SKIP]
The third moment integrates nicely with the help of Apery's constant
(zeta_three). Verify the result via quadrature.
* Implement kurtosis for the K-S distribution
Verify the result via quadrature.
