ANORIN

This function evaluates the inverse of the standard normal (Gaussian) cumulative distribution function.

Function Return Value

ANORIN — Function value. (Output)
The probability that a standard normal random variable takes a value less than or equal to ANORIN is P.

Required Arguments

P — Probability for which the inverse of the normal cumulative distribution function is to be evaluated. (Input)
P must be in the open interval (0.0, 1.0).

FORTRAN 90 Interface

Generic: ANORIN (P)

Specific: The specific interface names are S_ANORIN and D_ANORIN.

FORTRAN 77 Interface

Single: ANORIN (P)

Double: The double precision name is DNORIN.

Description

Function ANORIN evaluates the inverse of the cumulative distribution function, Φ, of a standard normal (Gaussian) random variable, that is, x =  ANORIN(P) = Φ−1(p), where

 

The value of the distribution function at the point x is the probability that the random variable takes a value less than or equal to x. The standard normal distribution has a mean of 0 and a variance of 1.

Example

In this example, we compute the point such that the probability is 0.9 that a standard normal random variable is less than or equal to this point.

 

USE UMACH_INT

USE ANORIN_INT

IMPLICIT NONE

INTEGER NOUT

REAL P, X

!

CALL UMACH (2, NOUT)

P = 0.9

X = ANORIN(P)

WRITE (NOUT,99999) X

99999 FORMAT (' The 90th percentile of a standard normal is ', F6.4)

END

Output

 

The 90th percentile of a standard normal is 1.2816