double cdf_std(x)
double x;
double inv_std(p)
double p;
p) for a given value of p (0 < p < 1-1.0E-15), where
inv_F is the inverse distribution function of the standardized
normal distribution.
Accuracy:
0 < p <= 1-1E-4: the accuracy of the machine
1-1E-4 < p <= 1-1E-8: 13-10 significant digits
1-1E-8 < p <= 1-1E-11: 9-5 significant digits
1-1E-11 < p <= 1-1E-15: 4-2 significant digits
double pdf_t(x,n)
double x,n;
x with n (n > 0)
degrees of freedom with the accuracy of the machine.
double cdf_t(x,n)
double x,n;
x with n (n >0) degrees of freedom.
Accuracy: 10-14 significant digits for |x| >= 1E-7 .
double inv_t(p,n)
double p,n;
p,n) for a given value of p (0 < p <= 1-1E-15), where
inv_F is the inverse distribution function of the Student's distribution
for n (n > 0) degrees of freedom.
Accuracy:
0.5+1E-4 <= p < 1-1E-7: over 10 significant digits
1-1E-7 <= p < 1-1E-9: 10-9 significant digits
1-1E-9 <= p < 1-1E-12: 8-5 significant digits
1-1E-12 < p <= 1-1E-15: 4-2 significant digits
Similar accuracy for 0 < p < 0.5 .
double pdf_chi2(x,n)
double x,n;
x
with n (n > 0) degrees of freedom with the accuracy of the machine.
double cdf_chi2(x,n,rel_error)
double x,n,rel_error;
x with n (n > 0) degrees of freedom.
Accuracy: determined by rel_error (1E-15 <= rel_error < 0.5) .
double inv_chi2(p,n)
double p,n;
p,n) for a given value of p (1E-6 <= p < 1-1E-6), where
inv_F is the inverse distribution function of
the chi-square distribution for n (n > 0) degrees of freedom.
Accuracy: over 10 significant digits.
double pdf_beta(x,a,b)
double x,a,b;
x and parameters a,b
(a,b > 0) with the accuracy of the machine.
double cdf_beta(x,a,b,rel_error)
double x,a,b,rel_error;
x and parameters a,b (a,b > 0).
Accuracy: determined by rel_error (1E-15 <= rel_error < 0.5) .
double inv_beta(p,a,b,s_digits)
double p,a,b;
int s_digits;
p,a,b) for a given value of p (0 < p <= 1-1E-15), where
inv_F is the inverse distribution function of the Beta distribution with
parameters a,b.
Accuracy: The number of significant digits is determined by s_digits
(2 <= s_digits <= 14).
double pdf_f(x,n1,n2)
double x,n1,n2;
x and n1 and n2 (n1,n2 > 0)
degrees of freedom with the accuracy of the machine.
double cdf_f(x,n1,n2,rel_error)
double x,n1,n2,rel_error;
returns the cumulative distribution function of the F distribution
for a value x and n1 and n2 (n1,n2 > 0) degrees of freedom.
Accuracy: same as in t distribution if n1 = 1 or n2 = 1.
Otherwise determined by rel_error (1E-15 <= rel_error < 0.5) .
double inv_f(p,n1,n2,s_digits)
double p,n1,n2;
int s_digits
p,n1,n2) for a given value of p (0 < p < 1), where inv_F
is the inverse distribution function of the F distribution for n1 and n2
(n1,n2 > 0) degrees of freedom.
Accuracy: same as in t distribution if n1 = 1 or n2 = 1.
Otherwise the number of significant digits is determined by s_digits
(2 <= s_digits <= 4).
double lg_gamma(x)
double x;