Program g08chfe

!     G08CHF Example Program Text
!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
      Use nag_library, Only: g05kff, g05sff, g08chf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: genid = 1, lseed = 1, mstate = 17,   &
                                          nin = 5, nout = 6, subid = -1
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: a2, aa2, beta, nupper, p, sa2, sbeta
      Integer                          :: i, ifail, j, k, lstate, n, nsim,     &
                                          n_pseudo
      Logical                          :: issort
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: x(:), xsim(:), y(:)
      Integer                          :: seed(lseed), state(17)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: exp, real, sum
!     .. Executable Statements ..
      Write (nout,*) 'G08CHF Example Program Results'
      Write (nout,*)

!     Skip heading in data file
      Read (nin,*)

!     Read number of observations
      Read (nin,*) n

!     Memory allocation
      Allocate (x(n),y(n))

!     Read observations
      Read (nin,*)(x(i),i=1,n)

!     Maximum likelihood estimate of mean
      beta = sum(x(1:n))/real(n,kind=nag_wp)

!     PIT, using exponential CDF with mean beta
      Do i = 1, n
        y(i) = 1.0E0_nag_wp - exp(-x(i)/beta)
      End Do

!     Let g08chf sort the (approximately) uniform variates
      issort = .False.

!     Calculate A-squared
      ifail = 0
      a2 = g08chf(n,issort,y,ifail)
      aa2 = (1.0E0_nag_wp+0.6E0_nag_wp/real(n,kind=nag_wp))*a2

!     Number of simulations
      nsim = 888

!     Generate exponential variates using a repeatable seed
      Allocate (xsim(n*nsim))
      seed(1) = 206033
      lstate = mstate
      ifail = 0
      Call g05kff(genid,subid,seed,lseed,state,lstate,ifail)
      n_pseudo = n*nsim
      ifail = 0
      Call g05sff(n_pseudo,beta,state,xsim,ifail)

!     Simulations loop
      nupper = 0.0E0_nag_wp
      Do j = 1, nsim
        k = (j-1)*n
!       Maximum likelihood estimate of mean
        sbeta = sum(xsim(k+1:k+n))/real(n,kind=nag_wp)
!       PIT
        Do i = 1, n
          y(i) = 1.0E0_nag_wp - exp(-xsim(k+i)/sbeta)
        End Do
!       Calculate A-squared
        ifail = 0
        sa2 = g08chf(n,issort,y,ifail)
        If (sa2>aa2) Then
          nupper = nupper + 1.0E0_nag_wp
        End If
      End Do

!     Simulated upper tail probability value
      p = nupper/real(nsim+1,kind=nag_wp)

!     Results
      Write (nout,'(1X,A,E11.4)')                                              &
        'H0: data from exponential distribution with mean', beta
      Write (nout,'(1X,A,1X,F8.4)') 'Test statistic, A-squared: ', a2
      Write (nout,'(1X,A,1X,F8.4)') 'Upper tail probability:    ', p

    End Program g08chfe