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program example_normal_cdf
use stdlib_random, only: random_seed
use stdlib_stats_distribution_normal, only: norm_cdf => cdf_normal, &
norm => rvs_normal
implicit none
real, dimension(2, 3, 4) :: x, mu, sigma
real :: xsum
complex :: loc, scale
integer :: seed_put, seed_get, i
seed_put = 1234567
call random_seed(seed_put, seed_get)
! standard normal cumulative probability at x=0.0
print *, norm_cdf(0.0, 0.0, 1.0)
! 0.500000000
! cumulative probability at x=2.0 with mu=-1.0 sigma=2.0
print *, norm_cdf(2.0, -1.0, 2.0)
! 0.933192849
! cumulative probability at x=1.0 with mu=1.0 and sigma=-1.0 (out of range)
print *, norm_cdf(1.0, 1.0, -1.0)
! NaN
! standard normal random variates array
x = reshape(norm(0.0, 1.0, 24), [2, 3, 4])
! standard normal cumulative array
mu(:, :, :) = 0.0
sigma(:, :, :) = 1.0
print *, norm_cdf(x, mu, sigma)
! 0.713505626 0.207069695 0.486513376 0.424511284 0.587328553
! 0.335559726 0.401470929 0.806552052 0.866687536 0.371323735
! 0.866228044 0.898046613 0.198435277 0.141147852 0.681565762
! 0.206268221 0.627057910 0.580759525 0.190364420 7.27325380E-02
! 7.08068311E-02 0.728241026 0.522919059 0.390097380
! cumulative probability array where sigma<=0.0 for certain elements
print *, norm_cdf([1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 0.0, -1.0])
! 0.500000000 NaN NaN
! `cdf_normal` is pure and, thus, can be called concurrently
xsum = 0.0
do concurrent (i=1:size(x,3))
xsum = xsum + sum(norm_cdf(x(:,:,i), mu(:,:,i), sigma(:,:,i)))
end do
print *, xsum
! 11.3751936
! complex normal cumulative distribution at x=(0.5,-0.5) with real part of
! mu=1.0, sigma=0.5 and imaginary part of mu=0.0, sigma=1.0
loc = (1.0, 0.0)
scale = (0.5, 1.0)
print *, norm_cdf((0.5, -0.5), loc, scale)
! 4.89511043E-02
end program example_normal_cdf
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