int main(){
int rep_ct = 10000;
gsl_rng *r = apop_rng_alloc(0);
apop_db_open("data-census.db");
gsl_vector *base_data = apop_query_to_vector("select in_per_capita from income where sumlevel+0.0 =40");
double RI = apop_query_to_float("select in_per_capita from income where sumlevel+0.0 =40 and geo_id2+0.0=44");
gsl_vector *boot_sample = gsl_vector_alloc(base_data->size);
gsl_vector *replications = gsl_vector_alloc(rep_ct);
for (int i=0; i< rep_ct; i++){
one_boot(base_data, r, boot_sample);
gsl_vector_set(replications, i, apop_mean(boot_sample));
}
double stderror = sqrt(apop_var(replications));
double mean = apop_mean(replications);
printf("mean: %g; standard error: %g; (RI-mean)/stderr: %g; p value: %g\n",
mean, stderror, (RI-mean)/stderror, 2*gsl_cdf_gaussian_Q(fabs(RI-mean), stderror));
}
void _fortetRHS(const double * ts, const int num_steps, double * Is, const int num_intervals,
const double * abgthphi,
double *rhs) {
const double alpha = abgthphi[0];
const double beta = abgthphi[1];
const double gamma = abgthphi[2];
const double theta = abgthphi[3];
const double phi = abgthphi[4];
const double TAU_TOLERANCE = 1e-5;
const double psi = atan(theta);
// sort is
gsl_sort(Is, 1, num_intervals);
double lt, lI, ltau, vthforward, vthbackward,numerator, denominator;
for (int tidx = 0; tidx < num_steps; ++tidx) {
lt = ts[tidx];
rhs[tidx] = .0;
vthforward = 1. - (alpha*(1 - exp(-lt)) +
gamma / sqrt(1.+theta*theta) * ( sin ( theta * ( lt + phi) - psi)
-exp(-lt)*sin(phi*theta - psi) ));
for (int idx = 0; idx < num_intervals; ++idx){
lI = Is[idx];
if(lI >= (lt - TAU_TOLERANCE)) break;
ltau = lt - lI;
vthbackward = 1. - (alpha*(1 - exp(-lI)) +
gamma / sqrt(1.+theta*theta) * ( sin ( theta * ( lI + phi) - psi)
-exp(-lI)*sin(phi*theta - psi) ));
numerator = (vthforward - vthbackward*exp(-ltau))*sqrt(2.);
denominator = beta * sqrt(1. - exp(-2*ltau));
rhs[tidx] += gsl_cdf_gaussian_Q(numerator/denominator, 1.0);
}//end per time loop
}//end all times loop
}
void _fortetError(const double * ts, const int num_steps, double * Is, const int num_intervals,
const double * abgthphi,
double *error) {
const double alpha = abgthphi[0];
const double beta = abgthphi[1];
const double gamma = abgthphi[2];
const double theta = abgthphi[3];
const double phi = abgthphi[4];
// printf("Fortet: theta=%.2f,gamma=%.2f\n", theta, gamma);
const double TAU_TOLERANCE = 1e-5;
const double psi = atan(theta);
//Sort is:
gsl_sort(Is, 1, num_intervals);
double lt, lI, ltau, vthforward, vthbackward;
double numerator, denominator, lhs;
double max_lhs = .0;
double normalizing_const = 1.0*num_intervals;
double exp_factor;
for (int tidx = 0; tidx < num_steps; ++tidx) {
lt = ts[tidx];
vthforward = 1. - (alpha*(1 - exp(-lt)) +
gamma / sqrt(1.+theta*theta) * ( sin ( theta * ( lt + phi) - psi)
-exp(-lt)*sin(phi*theta - psi) ));
//Calculate LHS:
numerator = vthforward * sqrt(2.);
denominator = beta * sqrt(1. - exp(-2.*lt));
lhs = gsl_cdf_gaussian_Q(numerator/denominator, 1.0);
max_lhs = GSL_MAX(lhs, max_lhs);
error[tidx] = lhs;
//Calculate RHS:
for (int idx = 0; idx < num_intervals; ++idx){
lI = Is[idx];
if(lI >= (lt - TAU_TOLERANCE)) break;
ltau = lt - lI;
exp_factor = exp(-lI);
vthbackward = 1. - (alpha*(1. - exp_factor) +
gamma / sqrt(1.+theta*theta) * ( sin ( theta * ( lI + phi) - psi)
-exp_factor*sin(phi*theta - psi) ));
exp_factor = exp(-ltau);
numerator = (vthforward - vthbackward*exp_factor)*sqrt(2.);
denominator = beta * sqrt(1. - exp_factor*exp_factor);
error[tidx] -= gsl_cdf_gaussian_Q(numerator/denominator, 1.0) / normalizing_const;
}//end rhs (intervals) loop
}//end error (time steps) loop
//scale by max_lhs:
for (int tidx = 0; tidx < num_steps; ++tidx) {
error[tidx] = fabs(error[tidx]) / max_lhs;
}
}
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);
}
}
