/* The DChoose() and FChoose() unit tests.
*/
static void
utest_choose(ESL_RANDOMNESS *r, int n, int nbins, int be_verbose)
{
double *pd = NULL;
float *pf = NULL;
int *ct = NULL;
int i;
double X2, diff, exp, X2p;
if ((pd = malloc(sizeof(double) * nbins)) == NULL) esl_fatal("malloc failed");
if ((pf = malloc(sizeof(float) * nbins)) == NULL) esl_fatal("malloc failed");
if ((ct = malloc(sizeof(int) * nbins)) == NULL) esl_fatal("malloc failed");
/* Sample a random multinomial probability vector. */
if (esl_dirichlet_DSampleUniform(r, nbins, pd) != eslOK) esl_fatal("dirichlet sample failed");
esl_vec_D2F(pd, nbins, pf);
/* Sample observed counts using DChoose(). */
esl_vec_ISet(ct, nbins, 0);
for (i = 0; i < n; i++)
ct[esl_rnd_DChoose(r, pd, nbins)]++;
/* X^2 test on those observed counts. */
for (X2 = 0., i=0; i < nbins; i++) {
exp = (double) n * pd[i];
diff = (double) ct[i] - exp;
X2 += diff*diff/exp;
}
if (esl_stats_ChiSquaredTest(nbins, X2, &X2p) != eslOK) esl_fatal("chi square eval failed");
if (be_verbose) printf("DChoose(): \t%g\n", X2p);
if (X2p < 0.01) esl_fatal("chi squared test failed");
/* Repeat above for FChoose(). */
esl_vec_ISet(ct, nbins, 0);
for (i = 0; i < n; i++)
ct[esl_rnd_FChoose(r, pf, nbins)]++;
for (X2 = 0., i=0; i < nbins; i++) {
exp = (double) n * pd[i];
diff = (double) ct[i] - exp;
X2 += diff*diff/exp;
}
if (esl_stats_ChiSquaredTest(nbins, X2, &X2p) != eslOK) esl_fatal("chi square eval failed");
if (be_verbose) printf("FChoose(): \t%g\n", X2p);
if (X2p < 0.01) esl_fatal("chi squared test failed");
free(pd);
free(pf);
free(ct);
return;
}
/* Function: esl_mixgev_FitGuess()
*
* Purpose: Make initial randomized guesses at the parameters
* of mixture GEV <mg>, using random number generator
* <r> and observed data consisting of <n> values
* <x[0..n-1]>. This guess is a suitable starting
* point for a parameter optimization routine, such
* as <esl_mixgev_FitComplete()>.
*
* Specifically, we estimate one 'central' guess
* for a single Gumbel fit to the data, using the
* method of moments. Then we add $\pm 10\%$ to that 'central'
* $\mu$ and $\lambda$ to get each component
* $\mu_i$ and $\lambda_i$. The $\alpha_i$ parameters
* are generated by sampling uniformly from $-0.1..0.1$.
* Mixture coefficients $q_i$ are sampled uniformly.
*
* Args: r - randomness source
* x - vector of observed data values to fit, 0..n-1
* n - number of values in <x>
* mg - mixture GEV to put guessed params into
*
* Returns: <eslOK> on success.
*/
int
esl_mixgev_FitGuess(ESL_RANDOMNESS *r, double *x, int n, ESL_MIXGEV *mg)
{
double mean, variance;
double mu, lambda;
int k;
esl_stats_DMean(x, n, &mean, &variance);
lambda = eslCONST_PI / sqrt(6.*variance);
mu = mean - 0.57722/lambda;
esl_dirichlet_DSampleUniform(r, mg->K, mg->q);
for (k = 0; k < mg->K; k++)
{
mg->mu[k] = mu + 0.2 * mu * (esl_random(r) - 0.5);
mg->lambda[k] = lambda + 0.2 * lambda * (esl_random(r) - 0.5);
if (mg->isgumbel[k]) mg->alpha[k] = 0.;
else mg->alpha[k] = 0.2 * (esl_random(r) - 0.5);
}
return eslOK;
}
