!write a program by fortran language to calculate Standardized Precipitation Evapotranspiration Index (SPEI) using GEV fitting
      program spei_calculation
      implicit none

      !Declare variables
      integer :: n, i, j, k, index
      real, dimension(:), allocatable :: precipitation, evapotranspiration, spei
      real :: mu, sigma, shape

      !Read number of data points
      read *, n

      !Allocate memory for arrays
      allocate(precipitation(n), evapotranspiration(n), spei(n))

      !Read precipitation and evapotranspiration data
      do i=1,n
        read *, precipitation(i), evapotranspiration(i)
      end do

      !Calculate SPEI values using GEV fitting
      do i=1,n
        index = i
        k = 0
        do j=1,n
          if (precipitation(j) - evapotranspiration(j) < precipitation(index) - evapotranspiration(index)) then
            index = j
            k = k + 1
          end if
        end do

        !GEV parameter estimation
        mu = sum(log(precipitation(index:index+k) - evapotranspiration(index:index+k))) / k
        sigma = sqrt(sum((log(precipitation(index:index+k) - evapotranspiration(index:index+k)) - mu)**2) / k)
        shape = ((3 * sum((log(precipitation(index:index+k) - evapotranspiration(index:index+k)) - mu) / sigma)) / k) / ((sum(((log(precipitation(index:index+k) - evapotranspiration(index:index+k)) - mu) / sigma)**3)) / k)

        !SPEI calculation
        spei(i) = (log(precipitation(i) - evapotranspiration(i)) - mu) / sigma + shape * ((log(precipitation(i) - evapotranspiration(i)) - mu) / sigma)

      end do

      !Print SPEI values
      do i=1,n
        write(*,*) spei(i)
      end do

      !Deallocate memory
      deallocate(precipitation, evapotranspiration, spei)

      end program spei_calculation