This function evaluates the inverse of the lognormal cumulative probability distribution function.

Function Return Value

ALNIN — Function value, the probability that a lognormal random variable takes a value less than or equal to the returned value is the input probability P.   (Output)

Required Arguments

P — Probability for which the inverse of the lognormal 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:                              ALNIN (P, AMU, SIGMA)

Specific:                             The specific interface names are S_ALNIN and D_ALNIN.

FORTRAN 77 Interface

Single:                                ALNIN (P, AMU, SIGMA)

Double:                              The double precision name is DLNIN.

Description

The function ALNIN evaluates the inverse distribution function of a lognormal random variable with location parameter AMU and scale parameter SIGMA. The probability that a standard lognormal random variable takes a value less than or equal to the returned value is P.

Example

In this example, we evaluate the inverse probability function at P = 0.25,  AMU = 0.0, SIGMA = 0.5.

 

      USE UMACH_INT
      USE ALNIN_INT
      IMPLICIT NONE

      INTEGER NOUT

      REAL X, AMU, SIGMA, P

      CALL UMACH(2, NOUT)

      P = .25

      AMU = 0.0

      SIGMA = 0.5

      X = ALNIN(P, AMU, SIGMA)

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

99999 FORMAT (' ALNIN(', F6.3, ', ', F4.2, ', ', F4.2, ') = ', F6.4)

      END

Output

 

ALNIN( 0.250, 0.00, 0.50) = 0.7137

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