IPHIC 3CW "30 July 2007" "mathcw-1.00"

Table of contents


NAME

iphicf, iphic, iphicl, iphicw, iphicq, iphicll, iphicdf, iphicd, iphicdl, iphicdll - inverse complementary cumulative distribution function of the standard normal distribution

SYNOPSIS

cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ]

#include <mathcw.h>

extern float iphicf (float x);

extern double iphic (double x);

extern long double iphicl (long double x);

extern __float80 iphicw (__float80 x);

extern __float128 iphicq (__float128 x);

extern long_long_double iphicll (long_long_double x);

extern decimal_float iphicdf (decimal_float x);

extern decimal_double iphicd (decimal_double x);

extern decimal_long_double iphicdl (decimal_long_double x);

extern decimal_long_long_double iphicdll (decimal_long_long_double x);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Compute the inverse of the complementary cumulative distribution function of the standard normal distribution, defined by
iphic(phic(x)) = x.
The complementary cumulative distribution function of the standard normal distribution is defined by

phic(x) = (1/sqrt(2pi)) integral(t = x:infinity) exp((-t**2)/2) dt
        = 1 - phi(x).
In mathematical text, phi(x) is written with an uppercase Greek phi: \(*F(x). phic(x) is written in a similar notation with subscript c.

The value of x in iphic(x) should be in the range [0, 1].


RETURN VALUES

For in-range arguments, the returned value is in the range [-Infinity, +Infinity]. Otherwise, the returned value is a quiet NaN.

ERRORS

For out-of-range, Infinity, and NaN arguments, the returned value is a quiet NaN, and errno is set to EDOM.

SEE ALSO

erf(3CW), erfc(3CW), ierf(3CW), ierfc(3CW), iphi(3CW), phi(3CW), phic(3CW).