LGNPPF Subroutine

lgnppf(3f) - [M_datapac:PERCENT_POINT] compute the lognormal percent
point function

   SUBROUTINE LGNPPF(P,Ppf)

    REAL(kind=wp),intent(in)  :: P
    REAL(kind=wp),intent(out) :: Ppf

LGNPPF(3f) computes the percent point function value for the lognormal
distribution.

The lognormal distribution used herein has mean = sqrt(e) = 1.64872127
and standard deviation = sqrt(e*(e-1)) = 2.16119742. This distribution
is defined for all positive X and has the probability density function

    f(X) = (1/(X*sqrt(2*pi))) * exp(-log(X)*log(X)/2)

The lognormal distribution used herein is the distribution of the
variate x = exp(z) where the variate z is normally distributed with
mean = 0 and standard deviation = 1.

Note that the percent point function of a distribution is identically
the same as the inverse cumulative distribution function of the
distribution.

P      The value (between 0.0 (exclusively) and 1.0 (exclusively))
       at which the percent point function is to be evaluated.

PPF    The percent point function value for the lognormal distribution

program demo_lgnppf
!@(#) line plotter graph of function
use M_datapac, only : lgnppf, plott, label
implicit none
integer,parameter :: n=200
real              :: x(n), y(n)
integer           :: i
   call label('lgnppf')
   x=[(real(i)/real(n+1),i=1,n)]
   do i=1,n
      call lgnppf(x(i),y(i))
   enddo
   call plott(x,y,n)
end program demo_lgnppf

 The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                   I-----------I-----------I-----------I-----------I
  0.9950249E+00 -                            X X   X    X          X
  0.9537728E+00 I                  XXXXXXX X
  0.9125207E+00 I               XXXX
  0.8712686E+00 I            XXX
  0.8300166E+00 I           XX
  0.7887645E+00 I         XX
  0.7475125E+00 -         X
  0.7062603E+00 I        X
  0.6650083E+00 I       XX
  0.6237562E+00 I       X
  0.5825042E+00 I      X
  0.5412520E+00 I      X
  0.5000000E+00 -     XX
  0.4587479E+00 I     X
  0.4174958E+00 I     X
  0.3762438E+00 I    XX
  0.3349917E+00 I    X
  0.2937396E+00 I    X
  0.2524875E+00 -   XX
  0.2112355E+00 I   X
  0.1699834E+00 I   X
  0.1287313E+00 I   X
  0.8747923E-01 I   X
  0.4622716E-01 I  XX
  0.4975124E-02 -  X
                   I-----------I-----------I-----------I-----------I
            0.7596E-01  0.3348E+01  0.6620E+01  0.9893E+01  0.1316E+02

The original DATAPAC library was written by James Filliben of the
Statistical Engineering Division, National Institute of Standards
and Technology.

John Urban, 2022.05.31

CC0-1.0