double discretegeometricaverage(int T, int M, int S0, int K, double sigma, double r){
double dt=(double)T/M;
double T1=T-(M*(M-1)*(4*M+1))/(6.*M*M)*dt;
double T2=T-(M-1)/2.*dt;
double A=exp(-r*(T-T2)-sigma*sigma*(T2-T1)/2.);
double d=(log((double)S0/K)+(r-0.5*sigma*sigma)*T2)/(sigma*sqrt(T1));
return S0*A*gsl_cdf_gaussian_P(d+sigma*sqrt(T1),1)-K*exp(-r*T)*gsl_cdf_gaussian_P(d,1);
}
double Model::n1PDF(double x, void *params) {
Eigen::VectorXd d = *(Eigen::VectorXd *)params;
if (fabs(x) < 1e-10) {
return 0;
}
// fptpdf and fptcdf assume these parameter values (i.e., x0max = 1, chi = 2,
// sdI = 1), so don't change them.
const double x0max = 1;
const double chi = 2;
const double sdI = 1;
double res = fptpdf(x, x0max, chi, d(0), sdI);
for (unsigned int i = 1; i < d.size(); i++) {
res *= 1 - fptcdf(x, x0max, chi, d(i), sdI);
}
double normaliser = 1;
for (unsigned int i = 0; i < d.size(); i++) {
normaliser *= gsl_cdf_gaussian_P(-d(i), sdI);
}
return res / (1 - normaliser);
}
void Xtest_eval(Xtest *xtest)
{
/*
* This routine evaluates the p-value from the xtest data.
* x, y, sigma all must be filled in by the calling routine.
*/
/*
xtest->pvalue =
0.5*gsl_sf_erfc((xtest->y - xtest->x)/(sqrt(2.0)*xtest->sigma));
xtest->pvalue =
1 - 0.5*gsl_sf_erfc((xtest->y - xtest->x)/(sqrt(2.0)*xtest->sigma));
xtest->pvalue =
gsl_sf_erfc(fabs(xtest->y - xtest->x)/(sqrt(2.0)*xtest->sigma));
*/
xtest->pvalue =
gsl_cdf_gaussian_P(xtest->y - xtest->x,xtest->sigma);
if(verbose == D_XTEST || verbose == D_ALL){
printf("# Xtest_eval(): x = %10.5f y = %10.5f sigma = %10.5f\n",
xtest->x, xtest->y, xtest->sigma);
printf("# Xtest_eval(): p-value = %10.5f\n",xtest->pvalue);
}
}
/*
** Draw randomly from gaussian distribution for every cell
*/
void
gaussian(float mean, float stdev, char type) {
printf("# Dysfunction gaussian(%0.4f, %0.4f) of ",mean, stdev);
switch (type) {
case DYSFUNCTION_HEIGHT : printf("height\n"); break;
case DYSFUNCTION_WIDTH : printf("spatial\n"); break;
case DYSFUNCTION_FIRE : printf("fire\n"); break;
}
printf("# Note indices start at 0, and dimensions of gcell array are %d * %d\n",X,Y);
for(int x = 0 ; x < X ; x++)
for(int y = 0 ; y < Y ; y++) {
float value;
if (stdev == 0)
value = mean;
else {
// XXX simple linear search with function calls. Can be sped up heaps!
value = (double)rand()/(double)RAND_MAX;
double p;
for(p = -mean ; p < 1 - mean; p += 0.00001)
if (gsl_cdf_gaussian_P(p, stdev) >= value)
break;
value = mean + p;
}
switch (type) {
case DYSFUNCTION_HEIGHT : printf("%3d %3d h %f\n",x,y,value); break;
case DYSFUNCTION_WIDTH : printf("%3d %3d w %f\n",x,y,value); break;
case DYSFUNCTION_FIRE : printf("%3d %3d f %f\n",x,y,value); break;
}
}
}//gaussian()
double Model::fptpdf(const double &z, const double &x0max, const double &chi,
const double &d, const double &sddrift) {
const double zs = z * sddrift;
const double zu = z * d;
const double chiminuszu = chi - zu;
const double chizu = chiminuszu / zs;
const double chizumax = (chiminuszu - x0max) / zs;
const double tmp1 =
d * (gsl_cdf_gaussian_P(chizu, 1) - gsl_cdf_gaussian_P(chizumax, 1));
const double tmp2 = sddrift * (gsl_ran_gaussian_pdf(chizumax, 1) -
gsl_ran_gaussian_pdf(chizu, 1));
double res = (tmp1 + tmp2) / x0max;
return res;
}
int main()
{
double bottom_tail;
bottom_tail = gsl_cdf_gaussian_P(-1.96, 1);
printf("Area between [-1.96, 1.96]: %g\n", 1-2*bottom_tail);
return 0;
}
double getpValue(double x,double mu,double a,double b,double ei)
{
double sigma=a*exp(-0.5*x)+b;
ei-=mu;
double p=0;
ei=fabs(ei);
p=gsl_cdf_gaussian_P(ei,sigma);
p=1-p;
return p;
}
double
Gaussian::Cdf(size_t dim_, double val_) const{
double nDevs = (val_ - GetMean(dim_))/GetStDev(dim_);
if (nDevs > fCdfCutOff)
return 1;
if(nDevs < -1 * fCdfCutOff)
return 0;
return gsl_cdf_gaussian_P(val_ - GetMean(dim_), GetStDev(dim_));
}
double Model::fptcdf(const double &z, const double &x0max, const double &chi,
const double &d, const double &sddrift) {
const double zs = z * sddrift;
const double zu = z * d;
const double chiminuszu = chi - zu;
const double xx = chiminuszu - x0max;
const double chizu = chiminuszu / zs;
const double chizumax = xx / zs;
const double tmp1 =
zs * (gsl_ran_gaussian_pdf(chizumax, 1) - gsl_ran_gaussian_pdf(chizu, 1));
const double tmp2 = xx * gsl_cdf_gaussian_P(chizumax, 1) -
chiminuszu * gsl_cdf_gaussian_P(chizu, 1);
double res = 1 + (tmp1 + tmp2) / x0max;
return res;
}
double continuousgeometricaverage(int T, int szero, int K, double sigma, double r){
double d=(log((double)szero/K)+0.5*(r-0.5*sigma*sigma)*T)/(sigma*sqrt(T/3.));
return szero*exp(-0.5*(r+1./6*sigma*sigma)*T)*gsl_cdf_gaussian_P(d+sigma*sqrt(T/3.),1)-K*exp(-r*T)*gsl_cdf_gaussian_P(d,1);
}
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);
}
}