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PoissonDirectSingle.f95
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PoissonDirectSingle.f95
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!Author: H. Paul Keeler, 2020.
!Website: hpaulkeeler.com
!Repository: github.com/hpaulkeeler/posts
!For more details, see post:
!hpaulkeeler.com/simulating-poisson-random-variables-in-fortran/
program test_poisson
implicit none
!lambda is the Poisson parameter (that is, its mean)
real,parameter :: lambda = 4.7
!number of variables
integer :: numbSim = 1000
real :: meanPoisson !(sample) mean
real :: varPoisson !(sample) variance
!declare functions
integer funPoissonSingle
real funUniformSingle
!START Collect statistists on Poisson variables
!initialize statistics
integer :: numbPoissonTemp
real :: sumPoisson = 0
real :: sumPoissonSquared = 0
!loop through for each random variable
integer :: i !count (loop) variable
do i = 1, numbSim
!generate a single poisson variable
numbPoissonTemp = funPoissonSingle(lambda)
!total sum of variables
sumPoisson = sumPoisson+numbPoissonTemp
!total sum of squared variables
sumPoissonSquared =sumPoissonSquared+ numbPoissonTemp**2
if (i <= 5) then
!print the first 5 numbers
print *, "One of the Poisson variables has the value ", numbPoissonTemp
end if
end do
!calculate statistics
meanPoisson = sumPoisson / numbSim
varPoisson = sumPoissonSquared / numbSim - meanPoisson**2
!print statistics
print *, "The average of the Poisson variables is ", meanPoisson
print *, "The variance of the Poisson variables is", varPoisson
print *, "For Poisson random variables, the mean and variance will agree more and more as the number of simulations increases."
!END Collect statistists on Poisson variables
end program test_poisson
!START Function definitions
!Uniform function -- returns a standard uniform random variable
function funUniformSingle() result(randUni)
implicit none
real randUni
call random_seed
call random_number(randUni)
end function
!Poisson function -- returns a single Poisson random variable
function funPoissonSingle(lambda) result(randPoisson)
implicit none
real, intent(in) :: lambda !input
real :: exp_lambda !constant for terminating loop
real :: randUni !uniform variable
real :: prodUni !product of uniform variables
integer :: randPoisson !Poisson variable
!declare functions
real funUniformSingle
exp_lambda= exp(-lambda) !calculate constant
!initialize variables
randPoisson = -1
prodUni = 1
do while (prodUni > exp_lambda)
randUni = funUniformSingle() !generate uniform variable
prodUni = prodUni * randUni !update product
randPoisson = randPoisson + 1 !increase Poisson variable
end do
end function
!END Function definitions