/* nag_anderson_darling_stat (g08chc) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 */
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagg05.h>
#include <nagg08.h>

int main(void)
{
  /* Scalars */
  double a2, aa2, beta, nupper, p, sa2, sbeta;
  const Integer lseed = 1, subid = -1;
  Integer exit_status = 0, i, j, k, lstate = 17, n, nsim, n_pseudo;
  /* Arrays */
  double *x = 0, *xsim = 0, *y = 0;
  Integer seed[1], state[17];
  /* NAG types */
  Nag_Boolean issort;
  NagError fail;

  printf("%s\n\n",
         "nag_anderson_darling_stat (g08chc) Example Program Results");

  /* Skip heading in data file */
  scanf("%*[^\n] ");

  /* Read number of observations */
  scanf("%" NAG_IFMT "", &n);
  scanf("%*[^\n] ");

  /* Memory allocation */
  if (!(x = NAG_ALLOC(n, double)) || !(y = NAG_ALLOC(n, double)))
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read observations */
  for (i = 0; i < n; i++) {
    scanf("%lf", x + i);
  }
  scanf("%*[^\n] ");

  /* Maximum likelihood estimate of mean */
  for (i = 0, beta = 0.0; i < n; i++) {
    beta += x[i];
  }
  beta /= (double) n;

  /* PIT, using exponential CDF with mean beta */
  for (i = 0; i < n; i++) {
    y[i] = 1.0 - exp(-x[i] / beta);
  }

  /* Let nag_anderson_darling_stat (g08chc) sort the (approximately)
     uniform variates */
  issort = Nag_FALSE;

  /* Calculate the Anderson-Darling goodness-of-fit test statistic */
  INIT_FAIL(fail);
  /* nag_anderson_darling_stat (g08chc) */
  a2 = nag_anderson_darling_stat(n, issort, y, &fail);

  /* Correction due to estimated mean */
  aa2 = (1.0 + 0.6 / (double) n) * a2;

  /* Number of simulations; a suitably high number */
  nsim = 888;

  /* Generate exponential variates using a repeatable seed */
  n_pseudo = n * nsim;
  if (!(xsim = NAG_ALLOC(n_pseudo, double)))
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  INIT_FAIL(fail);

  /* Initialize NAG's Basic pseudorandom number generator to give a
     repeatable sequence */
  seed[0] = 206033;
  /* nag_rand_init_repeatable (g05kfc) */
  nag_rand_init_repeatable(Nag_Basic, subid, (const Integer *) seed,
                           lseed, state, &lstate, &fail);

  /* Generate a vector of pseudorandom numbers from an exponential
     distribution */
  /* nag_rand_exp (g05sfc) */
  nag_rand_exp(n_pseudo, beta, state, xsim, &fail);

  /* Simulations loop */
  for (j = 0, nupper = 0.0; j < nsim; j++) {
    /* Index in the simulated data */
    k = j * n;

    /* Maximum likelihood estimate of mean */
    for (i = 0, sbeta = 0.0; i < n; i++) {
      sbeta += xsim[k + i];
    }
    sbeta /= (double) n;

    /* PIT */
    for (i = 0; i < n; i++) {
      y[i] = 1.0 - exp(-xsim[k + i] / sbeta);
    }

    /* Calculate A-squared */
    /* nag_anderson_darling_stat (g08chc) */
    sa2 = nag_anderson_darling_stat(n, issort, y, &fail);

    if (sa2 > aa2) {
      nupper++;
    }
  }

  /* Simulated upper tail probability value */
  p = nupper / (double) (nsim + 1);

  /* Results */
  printf("%s", " H0: data from exponential distribution with mean ");
  printf("%g\n", beta);
  printf("%s", " Test statistic, A-squared: ");
  printf("%6g\n", a2);
  printf("%s", " Upper tail probability:    ");
  printf("%6g\n", p);

END:
  NAG_FREE(x);
  NAG_FREE(xsim);
  NAG_FREE(y);

  return exit_status;
}