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
