/* nag_anderson_darling_stat (g08chc) Example Program. * * Mark 23 Release. NAG Copyright 2011. */ #include #include #include #include #include #include #include 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: if (x) NAG_FREE(x); if (xsim) NAG_FREE(xsim); if (y) NAG_FREE(y); return exit_status; }