double
gsl_cdf_binomial_Q (const unsigned int k, const double p, const unsigned int n)
{
double Q;
double a;
double b;
if (p > 1.0 || p < 0.0)
{
CDF_ERROR ("p < 0 or p > 1", GSL_EDOM);
}
if (k >= n)
{
Q = 0.0;
}
else
{
a = (double) k + 1.0;
b = (double) n - k;
Q = gsl_cdf_beta_P (p, a, b);
}
return Q;
}
static double
bisect (double x, double P, double a, double b, double xtol, double Ptol)
{
double x0 = 0, x1 = 1, Px;
while (fabs(x1 - x0) > xtol) {
Px = gsl_cdf_beta_P (x, a, b);
if (fabs(Px - P) < Ptol) {
/* return as soon as approximation is good enough, including on
the first iteration */
return x;
} else if (Px < P) {
x0 = x;
} else if (Px > P) {
x1 = x;
}
x = 0.5 * (x0 + x1);
}
return x;
}
double
gsl_cdf_negative_binomial_P (const unsigned int k, const double p, const double n)
{
double P;
double a;
double b;
if (p > 1.0 || p < 0.0)
{
CDF_ERROR ("p < 0 or p > 1", GSL_EDOM);
}
if (n < 0)
{
CDF_ERROR ("n < 0", GSL_EDOM);
}
a = (double) n;
b = (double) k + 1.0;
P = gsl_cdf_beta_P (p, a, b);
return P;
}
double
gsl_cdf_beta_Pinv (const double P, const double a, const double b)
{
double x, mean;
if (P < 0.0 || P > 1.0)
{
CDF_ERROR ("P must be in range 0 < P < 1", GSL_EDOM);
}
if (a < 0.0)
{
CDF_ERROR ("a < 0", GSL_EDOM);
}
if (b < 0.0)
{
CDF_ERROR ("b < 0", GSL_EDOM);
}
if (P == 0.0)
{
return 0.0;
}
if (P == 1.0)
{
return 1.0;
}
if (P > 0.5)
{
return gsl_cdf_beta_Qinv (1 - P, a, b);
}
mean = a / (a + b);
if (P < 0.1)
{
/* small x */
double lg_ab = gsl_sf_lngamma (a + b);
double lg_a = gsl_sf_lngamma (a);
double lg_b = gsl_sf_lngamma (b);
double lx = (log (a) + lg_a + lg_b - lg_ab + log (P)) / a;
if (lx <= 0) {
x = exp (lx); /* first approximation */
x *= pow (1 - x, -(b - 1) / a); /* second approximation */
} else {
x = mean;
}
if (x > mean)
x = mean;
}
else
{
/* Use expected value as first guess */
x = mean;
}
{
double lambda, dP, phi;
unsigned int n = 0;
start:
dP = P - gsl_cdf_beta_P (x, a, b);
phi = gsl_ran_beta_pdf (x, a, b);
if (dP == 0.0 || n++ > 64)
goto end;
lambda = dP / GSL_MAX (2 * fabs (dP / x), phi);
{
double step0 = lambda;
double step1 = -((a - 1) / x - (b - 1) / (1 - x)) * lambda * lambda / 2;
double step = step0;
if (fabs (step1) < fabs (step0))
{
step += step1;
}
else
{
/* scale back step to a reasonable size when too large */
step *= 2 * fabs (step0 / step1);
};
if (x + step > 0 && x + step < 1)
{
x += step;
}
else
{
x = sqrt (x) * sqrt (mean); /* try a new starting point */
}
if (fabs (step0) > 1e-10 * x)
goto start;
}
end:
return x;
}
}
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);
}
}