modified parameterisation for stats exp dist. procedures

Author: sebastian-mutz

example/stats_distribution_exponential/example_exponential_cdf.f90

@@ -4,60 +4,72 @@ program example_exponential_cdf
                                                    rexp => rvs_exp
 
   implicit none
-  real, dimension(2, 3, 4) :: x, lambda
+  real, dimension(2, 3, 4) :: x, loc, scale
   real :: xsum
-  complex :: scale
+  complex :: cloc, cscale
   integer :: seed_put, seed_get, i
 
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  ! standard exponential cumulative distribution at x=1.0
-  print *, exp_cdf(1.0, 1.0)
+  ! standard exponential cumulative distribution at x=1.0 with loc=0.0, scale=1.0
+  print *, exp_cdf(1.0, 0.0, 1.0)
   ! 0.632120550
 
-  ! cumulative distribution at x=2.0 with lambda=2
-  print *, exp_cdf(2.0, 2.0)
+  ! cumulative distribution at x=2.0 with loc=0.0 and scale=0.5 (equivalent of lambda=2)
+  print *, exp_cdf(2.0, 0.0, 0.5)
   ! 0.981684387
 
-  ! cumulative distribution at x=2.0 with lambda=-1.0 (out of range)
-  print *, exp_cdf(2.0, -1.0) 
+  ! cumulative distribution at x=2.5 with loc=0.5 and scale=0.5 (equivalent of lambda=2)
+  print *, exp_cdf(2.5, 0.5, 0.5)
+  ! 0.981684387
+
+  ! cumulative distribution at x=2.0 with loc=0.0 and scale=-1.0 (out of range)
+  print *, exp_cdf(2.0, 0.0, -1.0)
   ! NaN
 
+  ! cumulative distribution at x=0.5 with loc=1.0 and scale=1.0, putting x below the minimum
+  print *, exp_cdf(0.5, 1.0, 1.0)
+  ! 0.00000000
+
    ! standard exponential random variates array
-  x = reshape(rexp(0.5, 24), [2, 3, 4])
+  x = reshape(rexp(0.0, 2.0, 24), [2, 3, 4])
 
   ! a rank-3 exponential cumulative distribution
-  lambda(:, :, :) = 0.5
-  print *, exp_cdf(x, lambda)
+  loc(:, :, :)   = 0.0
+  scale(:, :, :) = 2.0
+  print *, exp_cdf(x, loc, scale)
   ! 0.301409245  0.335173965  5.94930053E-02  0.113003314
   ! 0.365694344  0.583515942  0.113774836     0.838585377
   ! 0.509324908  0.127967060  0.857194781     0.893231630
   ! 0.355383813  0.470882893  0.574203610     0.799321830
   ! 0.546216846  0.111995399  0.801794767     0.922525287
-  ! 0.937719882  0.301136374  3.44503522E-02  0.134661376 
+  ! 0.937719882  0.301136374  3.44503522E-02  0.134661376
+
 
-  ! cumulative distribution array where lambda<=0.0 for certain elements 
-  print *, exp_cdf([1.0, 1.0, 1.0], [1.0, 0.0, -1.0])
+  ! cumulative distribution array where scale<=0.0 for certain elements
+  print *, exp_cdf([1.0, 1.0, 1.0], [0.0, 0.0, 0.0], [1.0, 0.0, -1.0])
   ! 0.632120550  NaN NaN
 
-  ! `cdf_exp` is pure and, thus, can be called concurrently 
+  ! `cdf_exp` is pure and, thus, can be called concurrently
   xsum = 0.0
   do concurrent (i=1:size(x,3))
-    xsum = xsum + sum(exp_cdf(x(:,:,i), lambda(:,:,i)))
+    xsum = xsum + sum(exp_cdf(x(:,:,i), loc(:,:,i), scale(:,:,i)))
   end do
   print *, xsum
   ! 11.0886612
 
-  ! complex exponential cumulative distribution at (0.5,0.5) with real part of
-  ! lambda=0.5 and imaginary part of lambda=1.0
-  scale = (0.5, 1.0)
-  print *, exp_cdf((0.5, 0.5), scale)
+  ! complex exponential cumulative distribution at (0.5, 0.0, 2) with real part of
+  ! scale=2 and imaginary part of scale=1.0
+  cloc   = (0.0, 0.0)
+  cscale = (2, 1.0)
+  print *, exp_cdf((0.5, 0.5), cloc, cscale)
   ! 8.70351046E-02
 
-  ! As above, but with lambda%im < 0 
-  scale = (1.0, -2.0)
-  print *, exp_cdf((1.5, 1.0), scale)
+  ! As above, but with scale%im < 0
+  cloc   = (0.0, 0.0)
+  cscale = (1.0, -2.0)
+  print *, exp_cdf((1.5, 1.0), cloc, cscale)
   ! NaN
 
 end program example_exponential_cdf

example/stats_distribution_exponential/example_exponential_pdf.f90

@@ -4,59 +4,66 @@ program example_exponential_pdf
                                                     rexp => rvs_exp
 
   implicit none
-  real, dimension(2, 3, 4) :: x, lambda
+  real, dimension(2, 3, 4) :: x, loc, scale
   real :: xsum
-  complex :: scale
+  complex :: cloc, cscale
   integer :: seed_put, seed_get, i
 
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
-  ! probability density at x=1.0 in standard exponential
-  print *, exp_pdf(1.0, 1.0)
+  ! probability density at x=1.0 with loc=0 and in standard exponential
+  print *, exp_pdf(1.0, 0.0, 1.0)
   ! 0.367879450
 
-  ! probability density at x=2.0 with lambda=2.0
-  print *, exp_pdf(2.0, 2.0) 
+  ! probability density at x=2.0 with loc=0.0 and scale=0.5 (lambda=2.0)
+  print *, exp_pdf(2.0, 0.0, 0.5)
   ! 3.66312787E-02
 
-  ! probability density at x=2.0 with lambda=-1.0 (out of range)
-  print *, exp_pdf(2.0, -1.0) 
+  ! probability density at x=1.5 with loc=0.5 and scale=0.5 (lambda=2.0)
+  print *, exp_pdf(2.5, 0.5, 0.5)
+  ! 3.66312787E-02
+
+  ! probability density at x=2.0 with loc=0.0 and scale=-1.0 (out of range)
+  print *, exp_pdf(2.0, 0.0, -1.0)
   ! NaN
 
-  ! standard exponential random variates array  
-  x = reshape(rexp(0.5, 24), [2, 3, 4])
+  ! standard exponential random variates array
+  x = reshape(rexp(0.0, 2.0, 24), [2, 3, 4])
 
   ! a rank-3 exponential probability density
-  lambda(:, :, :) = 0.5
-  print *, exp_pdf(x, lambda)
+  loc(:, :, :)   = 0.0
+  scale(:, :, :) = 2.0
+  print *, exp_pdf(x, loc, scale)
   ! 0.349295378      0.332413018     0.470253497     0.443498343      0.317152828
   ! 0.208242029      0.443112582     8.07073265E-02  0.245337561      0.436016470
   ! 7.14025944E-02   5.33841923E-02  0.322308093     0.264558554      0.212898195
   ! 0.100339092      0.226891592     0.444002301     9.91026312E-02   3.87373678E-02
-  ! 3.11400592E-02   0.349431813     0.482774824     0.432669312     
+  ! 3.11400592E-02   0.349431813     0.482774824     0.432669312
 
-  ! probability density array where lambda<=0.0 for certain elements 
-  print *, exp_pdf([1.0, 1.0, 1.0], [1.0, 0.0, -1.0])
+  ! probability density array where scale<=0.0 for certain elements (loc = 0.0)
+  print *, exp_pdf([1.0, 1.0, 1.0], [0.0, 0.0, 0.0], [1.0, 0.0, -1.0])
   ! 0.367879450  NaN NaN
 
-  ! `pdf_exp` is pure and, thus, can be called concurrently 
+  ! `pdf_exp` is pure and, thus, can be called concurrently
   xsum = 0.0
   do concurrent (i=1:size(x,3))
-    xsum = xsum + sum(exp_pdf(x(:,:,i), lambda(:,:,i)))
+    xsum = xsum + sum(exp_pdf(x(:,:,i), loc(:,:,i), scale(:,:,i)))
   end do
   print *, xsum
   ! 6.45566940
 
-  ! complex exponential probability density function at (1.5,1.0) with real part
-  ! of lambda=1.0 and imaginary part of lambda=2.0
-  scale = (1.0, 2.)
-  print *, exp_pdf((1.5, 1.0), scale)
+  ! complex exponential probability density function at (1.5, 0.0, 1.0) with real part
+  ! of scale=1.0 and imaginary part of scale=0.5
+  cloc   = (0.0, 0.0)
+  cscale = (1.0, 0.5)
+  print *, exp_pdf((1.5, 1.0), cloc, cscale)
   ! 6.03947677E-02
 
-  ! As above, but with lambda%re < 0 
-  scale = (-1.0, 2.)
-  print *, exp_pdf((1.5, 1.0), scale)
+  ! As above, but with scale%re < 0
+  cloc   = (0.0, 0.0)
+  cscale = (-1.0, 2.0)
+  print *, exp_pdf((1.5, 1.0), cloc, cscale)
   ! NaN
 
 end program example_exponential_pdf

example/stats_distribution_exponential/example_exponential_rvs.f90

@@ -3,30 +3,28 @@ program example_exponential_rvs
   use stdlib_stats_distribution_exponential, only: rexp => rvs_exp
 
   implicit none
-  complex :: scale
+  complex :: cloc, cscale
   integer :: seed_put, seed_get
 
   seed_put = 1234567
   call random_seed(seed_put, seed_get)
 
   print *, rexp()         !single standard exponential random variate
-
 ! 0.358690143
 
-  print *, rexp(2.0)       !exponential random variate with lambda=2.0
-
-! 0.816459715
-
-  print *, rexp(0.3, 10)   !an array of 10 variates with lambda=0.3
+  print *, rexp(0.6, 0.2) !exponential random variate with loc=0.6 and scale=0.5 (lambda=2)
+! 0.681645989
 
-!  1.84008647E-02  3.59742008E-02  0.136567295  0.262772143  3.62352766E-02
-!  0.547133625  0.213591918  4.10784185E-02  0.583882213  0.671128035
+  print *, rexp(0.0, 3.0, 10)   !an array of 10 variates with loc=0.0 and scale=3.0 (lambda=1/3)
+! 0.184008643      0.359742016       1.36567295       2.62772131      0.362352759
+! 5.47133636       2.13591909      0.410784155       5.83882189       6.71128035
 
-  scale = (2.0, 0.7)
-  print *, rexp(scale)
-!single complex exponential random variate with real part of lambda=2.0;
-!imagainary part of lambda=0.7
+  cloc   = (0.0, 0.0)
+  cscale = (0.5, 1.6)
+  print *, rexp(cloc, cscale)
+!single complex exponential random variate with real part of scale=0.5 (lambda=2.0);
+!imagainary part of scale=1.6 (lambda=0.625)
 
-! (1.41435969,4.081114382E-02)
+! (0.219550118,1.01847279)
 
 end program example_exponential_rvs