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, 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
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