ALNDF

This function evaluates the lognormal cumulative probability distribution function.

Function Return Value

ALNDF — Function value, the probability that a standard lognormal random variable takes a value less than or equal to X. (Output)

Required Arguments

X — Argument for which the lognormal cumulative distribution function is to be evaluated. (Input)

AMU — Location parameter of the lognormal cumulative distribution function. (Input)

SIGMA — Shape parameter of the lognormal cumulative distribution function. SIGMA must be greater than 0. (Input)

FORTRAN 90 Interface

Generic: ALNDF (X, AMU, SIGMA)

Specific: The specific interface names are S_ALNDF and D_ALNDF.

FORTRAN 77 Interface

Single: ALNDF (X, AMU, SIGMA)

Double: The double precision name is DLNDF.

Description

The function ALNDF evaluates the lognormal cumulative probability distribution function, defined as

 

where

 

is the standard normal CDF.

Example

In this example, we evaluate the probability distribution function at X = 0.7137, AMU = 0.0,
SIGMA = 0.5.

 

USE UMACH_INT

USE ALNDF_INT

IMPLICIT NONE

INTEGER NOUT

REAL X, AMU, SIGMA, PR

CALL UMACH(2, NOUT)

X = .7137

AMU = 0.0

SIGMA = 0.5

PR = ALNDF(X, AMU, SIGMA)

WRITE (NOUT, 99999) X, AMU, SIGMA, PR

99999 FORMAT (' ALNDF(', F6.2, ', ', F4.2, ', ', F4.2, ') = ', F6.4)

END

Output

 

ALNDF( 0.71, 0.00, 0.50) = 0.2500