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

Table of contents


NAME

iphif, iphi, iphil, iphiw, iphiq, iphill, iphidf, iphid, iphidl, iphidll - inverse 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 iphif (float x);

extern double iphi (double x);

extern long double iphil (long double x);

extern __float80 iphiw (__float80 x);

extern __float128 iphiq (__float128 x);

extern long_long_double iphill (long_long_double x);

extern decimal_float iphidf (decimal_float x);

extern decimal_double iphid (decimal_double x);

extern decimal_long_double iphidl (decimal_long_double x);

extern decimal_long_long_double iphidll (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 cumulative distribution function of the standard normal distribution, defined by
iphi(phi(x)) = x.
The cumulative distribution function of the standard normal distribution is defined by

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

The value of x in iphi(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), iphic(3CW), phi(3CW), phic(3CW).