LAMSF Subroutine

lamsf(3f) - [M_datapac:SPARSITY] compute the Tukey-Lambda sparsity
function

   SUBROUTINE LAMSF(P,Alamba,Sf)

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

LAMSF(3f) computes the sparsity function value for the (Tukey) lambda
distribution with tail length parameter value = ALAMBA.

In general, the probability density function for this distribution
is not simple.

The percent point function for this distribution is

    g(P) = ((P**ALAMBA)-((1-P)**ALAMBA))/ALAMBA

Note that the sparsity function of a distribution is the derivative
of the percent point function, and also is the reciprocal of the
probability density function (but in units of P rather than X).

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

ALAMBA  The value of Lambda (the Tail Length parameter).

        If ALAMBA is positive, then P should be between 0.0 and 1.0,
        inclusively.

        If ALAMBA is non-positive, then P should be between 0.0 and
        1.0, exclusively.

SF      The sparsity function value for the Tukey Lambda distribution

program demo_lamsf
use M_datapac, only : lamsf
implicit none
! call lamsf(x,y)
end program demo_lamsf

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

lgncdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the lognormal
cumulative distribution function

   SUBROUTINE LGNCDF(X,Cdf)

    REAL(kind=wp),intent(in)  :: X
    REAL(kind=wp),intent(out) :: Cdf

LGNCDF(3f) computes the cumulative distribution 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.

X      The value at which the cumulative distribution function is
       to be evaluated. X should be positive.

Cdf    The cumulative distribution function value for the lognormal
       distribution

program demo_lgncdf
!@(#) line plotter graph of cumulative distribution function
use M_datapac, only : lgncdf, plott, label
implicit none
real,allocatable  :: x(:), y(:)
integer           :: i
   call label('lgncdf')
   x=[((real(i)+epsilon(0.0))/10.0,i=0,100,1)]
   if(allocated(y))deallocate(y)
   allocate(y(size(x)))
   do i=1,size(x)
      call lgncdf(x(i),y(i))
   enddo
   call plott(x,y,size(x))
end program demo_lgncdf

 The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                   I-----------I-----------I-----------I-----------I
  0.1000000E+02 -                                                  X
  0.9583333E+01 I                                                  X
  0.9166667E+01 I                                                  X
  0.8750000E+01 I                                                  X
  0.8333333E+01 I                                                  X
  0.7916667E+01 I                                                  X
  0.7500000E+01 -                                                 XX
  0.7083333E+01 I                                                 X
  0.6666667E+01 I                                                 X
  0.6250000E+01 I                                                 X
  0.5833333E+01 I                                                 X
  0.5416667E+01 I                                                X
  0.5000000E+01 -                                                X
  0.4583333E+01 I                                               XX
  0.4166667E+01 I                                              XX
  0.3750000E+01 I                                              X
  0.3333333E+01 I                                             X
  0.2916667E+01 I                                           XX
  0.2500000E+01 -                                         XXX
  0.2083333E+01 I                                      XXX
  0.1666667E+01 I                                  XXXX
  0.1250000E+01 I                            X XX X
  0.8333340E+00 I                   X  X X X
  0.4166670E+00 I        X  X  X  X
  0.1192093E-07 -  XX X
                   I-----------I-----------I-----------I-----------I
            0.0000E+00  0.2473E+00  0.4947E+00  0.7420E+00  0.9893E+00

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