double
test_tdist2_pdf (double x)
{
return gsl_ran_tdist_pdf (x, 12.75);
}
double
tdist (double x, void *p)
{
double * c = (double *)p;
return gsl_ran_tdist_pdf (x, c[0]);
}
double
gsl_cdf_tdist_Pinv (const double P, const double nu)
{
double x, ptail;
if (P == 1.0)
{
return GSL_POSINF;
}
else if (P == 0.0)
{
return GSL_NEGINF;
}
if (nu == 1.0)
{
x = tan (M_PI * (P - 0.5));
return x;
}
else if (nu == 2.0)
{
x = (2 * P - 1) / sqrt (2 * P * (1 - P));
return x;
}
ptail = (P < 0.5) ? P : 1 - P;
if (sqrt (M_PI * nu / 2) * ptail > pow (0.05, nu / 2))
{
double xg = gsl_cdf_ugaussian_Pinv (P);
x = inv_cornish_fisher (xg, nu);
}
else
{
/* Use an asymptotic expansion of the tail of integral */
double beta = gsl_sf_beta (0.5, nu / 2);
if (P < 0.5)
{
x = -sqrt (nu) * pow (beta * nu * P, -1.0 / nu);
}
else
{
x = sqrt (nu) * pow (beta * nu * (1 - P), -1.0 / nu);
}
/* Correct nu -> nu/(1+nu/x^2) in the leading term to account
for higher order terms. This avoids overestimating x, which
makes the iteration unstable due to the rapidly decreasing
tails of the distribution. */
x /= sqrt (1 + nu / (x * x));
}
{
double dP, phi;
unsigned int n = 0;
start:
dP = P - gsl_cdf_tdist_P (x, nu);
phi = gsl_ran_tdist_pdf (x, nu);
if (dP == 0.0 || n++ > 32)
goto end;
{
double lambda = dP / phi;
double step0 = lambda;
double step1 = ((nu + 1) * x / (x * x + nu)) * (lambda * lambda / 4.0);
double step = step0;
if (fabs (step1) < fabs (step0))
{
step += step1;
}
if (P > 0.5 && x + step < 0)
x /= 2;
else if (P < 0.5 && x + step > 0)
x /= 2;
else
x += step;
if (fabs (step) > 1e-10 * fabs (x))
goto start;
}
end:
if (fabs(dP) > GSL_SQRT_DBL_EPSILON * P)
{
GSL_ERROR_VAL("inverse failed to converge", GSL_EFAILED, GSL_NAN);
}
return x;
}
}
double
gsl_cdf_tdist_Qinv (const double Q, const double nu)
{
double x, qtail;
if (Q == 0.0)
{
return GSL_POSINF;
}
else if (Q == 1.0)
{
return GSL_NEGINF;
}
if (nu == 1.0)
{
x = tan (M_PI * (0.5 - Q));
return x;
}
else if (nu == 2.0)
{
x = (1 - 2 * Q) / sqrt (2 * Q * (1 - Q));
return x;
}
qtail = (Q < 0.5) ? Q : 1 - Q;
if (sqrt (M_PI * nu / 2) * qtail > pow (0.05, nu / 2))
{
double xg = gsl_cdf_ugaussian_Qinv (Q);
x = inv_cornish_fisher (xg, nu);
}
else
{
/* Use an asymptotic expansion of the tail of integral */
double beta = gsl_sf_beta (0.5, nu / 2);
if (Q < 0.5)
{
x = sqrt (nu) * pow (beta * nu * Q, -1.0 / nu);
}
else
{
x = -sqrt (nu) * pow (beta * nu * (1 - Q), -1.0 / nu);
}
/* Correct nu -> nu/(1+nu/x^2) in the leading term to account
for higher order terms. This avoids overestimating x, which
makes the iteration unstable due to the rapidly decreasing
tails of the distribution. */
x /= sqrt (1 + nu / (x * x));
}
{
double dQ, phi;
unsigned int n = 0;
start:
dQ = Q - gsl_cdf_tdist_Q (x, nu);
phi = gsl_ran_tdist_pdf (x, nu);
if (dQ == 0.0 || n++ > 32)
goto end;
{
double lambda = - dQ / phi;
double step0 = lambda;
double step1 = ((nu + 1) * x / (x * x + nu)) * (lambda * lambda / 4.0);
double step = step0;
if (fabs (step1) < fabs (step0))
{
step += step1;
}
if (Q < 0.5 && x + step < 0)
x /= 2;
else if (Q > 0.5 && x + step > 0)
x /= 2;
else
x += step;
if (fabs (step) > 1e-10 * fabs (x))
goto start;
}
}
end:
return x;
}
static double one_t(double in, void *params){
double mu = ((double*)params)[0];
double sigma = ((double*)params)[1];
double df = ((double*)params)[2];
return log(gsl_ran_tdist_pdf((in-mu)/(sigma/sqrt(df)), df));
}
int main(int argc, char **argv){
distlist distribution = Normal;
char msg[10000], c;
int pval = 0, qval = 0;
double param1 = GSL_NAN, param2 =GSL_NAN, findme = GSL_NAN;
char number[1000];
sprintf(msg, "%s [opts] number_to_lookup\n\n"
"Look up a probability or p-value for a given standard distribution.\n"
"[This is still loosely written and counts as beta. Notably, negative numbers are hard to parse.]\n"
"E.g.:\n"
"%s -dbin 100 .5 34\n"
"sets the distribution to a Binomial(100, .5), and find the odds of 34 appearing.\n"
"%s -p 2 \n"
"find the area of the Normal(0,1) between -infty and 2. \n"
"\n"
"-pval Find the p-value: integral from -infinity to your value\n"
"-qval Find the q-value: integral from your value to infinity\n"
"\n"
"After giving an optional -p or -q, specify the distribution. \n"
"Default is Normal(0, 1). Other options:\n"
"\t\t-binom Binomial(n, p)\n"
"\t\t-beta Beta(a, b)\n"
"\t\t-f F distribution(df1, df2)\n"
"\t\t-norm Normal(mu, sigma)\n"
"\t\t-negative bin Negative binomial(n, p)\n"
"\t\t-poisson Poisson(L)\n"
"\t\t-t t distribution(df)\n"
"I just need enough letters to distinctly identify a distribution.\n"
, argv[0], argv[0], argv[0]);
opterr=0;
if(argc==1){
printf("%s", msg);
return 0;
}
while ((c = getopt (argc, argv, "B:b:F:f:N:n:pqT:t:")) != -1){
switch (c){
case 'B':
case 'b':
if (optarg[0]=='i')
distribution = Binomial;
else if (optarg[0]=='e')
distribution = Beta;
else {
printf("I can't parse the option -b%s\n", optarg);
exit(0);
}
param1 = atof(argv[optind]);
param2 = atof(argv[optind+1]);
findme = atof(argv[optind+2]);
break;
case 'F':
case 'f':
distribution = F;
param1 = atof(argv[optind]);
findme = atof(argv[optind+1]);
break;
case 'H':
case 'h':
printf("%s", msg);
return 0;
case 'n':
case 'N':
if (optarg[0]=='o'){ //normal
param1 = atof(argv[optind]);
param2 = atof(argv[optind+1]);
findme = atof(argv[optind+2]);
} else if (optarg[0]=='e'){
distribution = Negbinom;
param1 = atof(argv[optind]);
param2 = atof(argv[optind+1]);
findme = atof(argv[optind+2]);
} else {
printf("I can't parse the option -n%s\n", optarg);
exit(0);
}
break;
case 'p':
if (!optarg || optarg[0] == 'v')
pval++;
else if (optarg[0] == 'o'){
distribution = Poisson;
param1 = atof(argv[optind]);
findme = atof(argv[optind+1]);
} else {
printf("I can't parse the option -p%s\n", optarg);
exit(0);
}
break;
case 'q':
qval++;
break;
case 'T':
case 't':
distribution = T;
param1 = atof(argv[optind]);
findme = atof(argv[optind+1]);
break;
case '?'://probably a negative number
if (optarg)
snprintf(number, 1000, "%c%s", optopt, optarg);
else snprintf(number, 1000, "%c", optopt);
if (gsl_isnan(param1)) param1 = -atof(number);
else if (gsl_isnan(param2)) param2 = -atof(number);
else if (gsl_isnan(findme)) findme = -atof(number);
}
}
if (gsl_isnan(findme)) findme = atof(argv[optind]);
//defaults, as promised
if (gsl_isnan(param1)) param1 = 0;
if (gsl_isnan(param2)) param2 = 1;
if (!pval && !qval){
double val =
distribution == Beta ? gsl_ran_beta_pdf(findme, param1, param2)
: distribution == Binomial ? gsl_ran_binomial_pdf(findme, param2, param1)
: distribution == F ? gsl_ran_fdist_pdf(findme, param1, param2)
: distribution == Negbinom ? gsl_ran_negative_binomial_pdf(findme, param2, param1)
: distribution == Normal ? gsl_ran_gaussian_pdf(findme, param2)+param1
: distribution == Poisson ? gsl_ran_poisson_pdf(findme, param1)
: distribution == T ? gsl_ran_tdist_pdf(findme, param1) : GSL_NAN;
printf("%g\n", val);
return 0;
}
if (distribution == Binomial){
printf("Sorry, the GSL doesn't have a Binomial CDF.\n");
return 0; }
if (distribution == Negbinom){
printf("Sorry, the GSL doesn't have a Negative Binomial CDF.\n");
return 0; }
if (distribution == Poisson){
printf("Sorry, the GSL doesn't have a Poisson CDF.\n");
return 0; }
if (pval){
double val =
distribution == Beta ? gsl_cdf_beta_P(findme, param1, param2)
: distribution == F ? gsl_cdf_fdist_P(findme, param1, param2)
: distribution == Normal ? gsl_cdf_gaussian_P(findme-param1, param2)
: distribution == T ? gsl_cdf_tdist_P(findme, param1) : GSL_NAN;
printf("%g\n", val);
return 0;
}
if (qval){
double val =
distribution == Beta ? gsl_cdf_beta_Q(findme, param1, param2)
: distribution == F ? gsl_cdf_fdist_Q(findme, param1, param2)
: distribution == Normal ? gsl_cdf_gaussian_Q(findme-param1, param2)
: distribution == T ? gsl_cdf_tdist_Q(findme, param1) : GSL_NAN;
printf("%g\n", val);
}
}
double skew_student(double x, double mu, double sig, double skew, double nu){
return 2.*gsl_ran_tdist_pdf((x-mu)/sig, nu)* \
gsl_cdf_tdist_P(skew*((x-mu)/sig)*sqrt((nu+1.)/(nu+(x-mu)*(x-mu)/sig/sig)),(nu+1.))/sig;}
