## Functions in library DISTRIB.LIB

##### cdf_std

``````double cdf_std(x)
double x;
``````
returns the cumulative distribution function of the standardized normal distribution with the accuracy of the machine.
##### inv_std

``````double inv_std(p)
double p;
``````
returns x = inv_F(`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

##### pdf_t

``````double pdf_t(x,n)
double x,n;
``````
returns the Student's density function for a value `x` with `n` (`n` > 0) degrees of freedom with the accuracy of the machine.
##### cdf_t

``````double cdf_t(x,n)
double x,n;
``````
returns the cumulative distribution function of the Student's distribution for a value `x` with `n` (`n` >0) degrees of freedom.

Accuracy: 10-14 significant digits for |`x`| >= 1E-7 .

##### inv_t

``````double inv_t(p,n)
double p,n;
``````
returns x = inv_F(`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 .

##### pdf_chi2

``````double pdf_chi2(x,n)
double x,n;
``````
returns the chi-square density function for a value `x` with `n` (`n` > 0) degrees of freedom with the accuracy of the machine.
##### cdf_chi2

``````double cdf_chi2(x,n,rel_error)
double x,n,rel_error;
``````
returns the cumulative distribution function of the chi-square distribution for a value `x` with `n` (`n` > 0) degrees of freedom.

Accuracy: determined by `rel_error` (1E-15 <= `rel_error` < 0.5) .

##### inv_chi2

``````double inv_chi2(p,n)
double p,n;
``````
returns x = inv_F(`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.

##### pdf_beta

``````double pdf_beta(x,a,b)
double x,a,b;
``````
returns the Beta density function for a value `x` and parameters `a`,`b` (`a`,`b` > 0) with the accuracy of the machine.
##### cdf_beta

``````double cdf_beta(x,a,b,rel_error)
double x,a,b,rel_error;
``````
returns the cumulative distribution function of the Beta distribution for a value `x` and parameters `a`,`b` (`a`,`b` > 0).

Accuracy: determined by `rel_error` (1E-15 <= `rel_error` < 0.5) .

##### inv_beta

``````double inv_beta(p,a,b,s_digits)
double p,a,b;
int s_digits;
``````
returns x = inv_F(`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).

##### pdf_f

``````double pdf_f(x,n1,n2)
double x,n1,n2;
``````
returns the F density function for a value `x` and `n1` and `n2` (`n1`,`n2` > 0) degrees of freedom with the accuracy of the machine.
##### cdf_f

``````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) .

##### inv_f

``````double inv_f(p,n1,n2,s_digits)
double p,n1,n2;
int s_digits
``````
returns x = inv_F(`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).

##### lg_gamma

``````double lg_gamma(x)
double x;
``````
returns the natural logarithm of the gamma function with the accuracy of the machine.

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