WEIPPF Subroutine

weippf(3f) - [M_datapac:PERCENT_POINT] compute the Weibull percent
point function

   SUBROUTINE WEIPPF(P,Gamma,Ppf)

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

WEIPPf(3f) computes the percent point function value for the Weibull
distribution with REAL tail length parameter = GAMMA.

The Weibull distribution used herein is defined for all positive X,
and has the probability density function

    f(X) = GAMMA * (X**(GAMMA-1)) * exp(-(X**GAMMA))

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 (inclusively) and 1.0 (exclusively))
       at which the percent point function is to be evaluated.

GAMMA  The value of the tail length parameter. GAMMA should be positive.

PPF    The percent point function value for the Weibull distribution

program demo_weippf
!@(#) line plotter graph of function
use M_datapac, only : weippf, plott, label
implicit none
integer,parameter :: n=200
real              :: x(n), y(n)
real              :: gamma
integer           :: i
   gamma=2.0
   call label('weippf')
   x=[(real(i)/real(n+1),i=1,n)]
   do i=1,n
      call weippf(x(i),gamma,y(i))
   enddo
   call plott(x,y,n)
end program demo_weippf

 The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                   I-----------I-----------I-----------I-----------I
  0.9950249E+00 -                                          XX X X  X
  0.9537728E+00 I                                    XXXXXX
  0.9125207E+00 I                                 XXXX
  0.8712686E+00 I                              XXX
  0.8300166E+00 I                            XXX
  0.7887645E+00 I                           XX
  0.7475125E+00 -                         XX
  0.7062603E+00 I                        XX
  0.6650083E+00 I                      XX
  0.6237562E+00 I                     XX
  0.5825042E+00 I                    XX
  0.5412520E+00 I                   XX
  0.5000000E+00 -                  XX
  0.4587479E+00 I                 XX
  0.4174958E+00 I                XX
  0.3762438E+00 I               XX
  0.3349917E+00 I              XX
  0.2937396E+00 I             XX
  0.2524875E+00 -            XX
  0.2112355E+00 I          XX
  0.1699834E+00 I         XX
  0.1287313E+00 I        XX
  0.8747923E-01 I      XXX
  0.4622716E-01 I    XXX
  0.4975124E-02 -  XXX
                   I-----------I-----------I-----------I-----------I
            0.7062E-01  0.6287E+00  0.1187E+01  0.1745E+01  0.2303E+01

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