analistica/ex-1/tests.h

/* This file contains functions to perform
 * statistical tests on the points sampled
 * from a Landau distribution.
 */

#include <gsl/gsl_rng.h>
#include <gsl/gsl_roots.h>

#pragma once

/* Kolmogorov distribution CDF
 * for sample size n and statistic D
 */
double kolmogorov_cdf(double D, int n);


/* Numerically computes the mode of a Landau
 * distribution by maximising the derivative.
 * The `min,max` parameters are the initial search
 * interval for the optimisation.
 *
 * If `err` is true print the estimate error.
 */
double numeric_mode(double min, double max,
                    gsl_function *pdf,
                    int err);


/* Numerically computes the FWHM of a PDF
 * distribution using the definition.
 * The `min,max` parameters are the initial search
 * interval for the root search of equation
 * `fwhm_equation`. Two searches are performed in
 * [min, mode] and [mode, max] that will give the
 * two solutions x₋, x₊. The FWHM is then x₊-x₋.
 *
 * If `err` is true print the estimate error.
 */
double numeric_fwhm(double min, double max,
                    gsl_function *pdf,
                    int err);


/* Trapani infinite moment test
 *
 * Tests whether the `order`-th moment of the
 * distribution of `sample` is infinite.
 * The test generates an artificial sample of
 * r points, where r = n^θ and returns a p-value.
 */
double trapani(gsl_rng *rng, double theta, double psi,
               int order, double *sample, size_t n);