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Author: Jim-215-Fisher

doc/specs/stdlib_stats_distribution_exponential.md

@@ -2,7 +2,7 @@
 title: stats_distribution
 ---
 
-# Statistical Distributions -- Exponential Distribution Module
+# Statistical Distributions -- Exponential Module
 
 [TOC]
 
@@ -22,33 +22,31 @@ With single argument, the function returns an exponential distributed random var
 
 With two auguments the function returns a rank one array of random variates.
 
-The rate parameter `lamda` must be greater than 0.
-
 ### Syntax
 
-`result = [[stdlib_stats_distribution_expon(module):exponential_distribution_rvs(interface)]]([lamda] [[, array_size]])`
+`result = [[stdlib_stats_distribution_exponential(module):exponential_distribution_rvs(interface)]]([lamda] [[, array_size]])`
 
 ### Arguments
 
-`lamda`: optional argument has `intent(in)` and is a scalar of type `real` or `complx`.
+`lamda`: optional argument has `intent(in)` and is a scalar of type `real` or `complex`.
 
 `array_size`: optional argument has `intent(in)` and is a scalar of type `integer`.
 
 ### Return value
 
-The result is a scalar or rank one array, with a size of `array_size`, of type `real` or `complx`.
+The result is a scalar or rank one array, with a size of `array_size`, of type `real` or `complex`.
 
 ### Example
 
 ```fortran
 program demo_exponential_rvs
     use stdlib_stats_distribution_PRNG, only : random_seed
-    use stdlib_stats_distribution_expon, only:                                  &
-        rexp => exponential_distribution_rvs
+    use stdlib_stats_distribution_exponential, only:                            &
+                                            rexp => exponential_distribution_rvs
 
     implicit none
     real ::  a(2,3,4)
-    complx :: scale
+    complex :: scale
     integer :: seed_put, seed_get
 
     seed_put = 1234567
@@ -64,20 +62,22 @@ program demo_exponential_rvs
 
     print *, rexp(0.3, 10)   !an array of 10 variates with lamda=0.3
 
-! [1.84008647E-02, 3.59742008E-02, 0.136567295, 0.262772143, 3.62352766E-02,
-!  0.547133625, 0.213591918, 4.10784185E-02, 0.583882213, 0.671128035]
+!  1.84008647E-02  3.59742008E-02  0.136567295  0.262772143  3.62352766E-02 
+!  0.547133625  0.213591918  4.10784185E-02  0.583882213  0.671128035
 
     a(:,:,:) = 0.5
     print *, rexp(a)         !a rank 3 array of 24 exponential random variates
 
-! [0.219550118, 0.318272740, 0.426896989, 0.803026378, 0.395067871,
-!  5.93891777E-02, 0.809226036, 1.27890170, 1.38805652, 0.179149821,
-!  1.75288841E-02, 7.23171830E-02, 0.157068044, 0.153069839, 0.421180248,
-!  0.517792642, 2.09411430, 0.785641313, 0.116311245, 0.295113146,
-!  0.824005902, 0.123385273, 5.50238751E-02, 3.52851897E-02]
+!  0.219550118  0.318272740  0.426896989  0.803026378  0.395067871 
+!  5.93891777E-02  0.809226036  1.27890170  1.38805652  0.179149821 
+!  1.75288841E-02  7.23171830E-02  0.157068044  0.153069839  0.421180248 
+!  0.517792642  2.09411430  0.785641313  0.116311245  0.295113146 
+!  0.824005902  0.123385273  5.50238751E-02  3.52851897E-02
 
     scale = (2.0, 0.7)
-    print *, rexp(scale)     !single complex exponential random variate with real part of lamda=2.0; imagainary part of lamda=0.7
+    print *, rexp(scale)
+    !single complex exponential random variate with real part of lamda=2.0;
+    !imagainary part of lamda=0.7
 
 ! (1.41435969,4.081114382E-02)
 
@@ -96,17 +96,15 @@ The probability density function of the continuous exponential distribution.
 
 $$ f(x)=\begin{cases}lamda \times e^{-lamda \times x} &x\geqslant 0 \\\\ 0 &x< 0\end{} $$
 
-x is supported on [0, \infty)
-
 ### Syntax
 
-`result = [[stdlib_stats_distribution_expon(module):exponential_distribution_pdf(interface)]](x, lamda)`
+`result = [[stdlib_stats_distribution_exponential(module):exponential_distribution_pdf(interface)]](x, lamda)`
 
 ### Arguments
 
-`x`: has `intent(in)` and is a scalar of type `real` or `complx`.
+`x`: has `intent(in)` and is a scalar of type `real` or `complex`.
 
-`lamda`: has `intent(in)` and is a scalar of type `real` or `complx`.
+`lamda`: has `intent(in)` and is a scalar of type `real` or `complex`.
 
 The function is elemental, i.e., all auguments could be arrays conformable to each other. All arguments must have the same type.
 
@@ -119,13 +117,13 @@ The result is a scalar or an array, with a shape conformable to auguments, of ty
 ```fortran
 program demo_exponential_pdf
     use stdlib_stats_distribution_PRNG, only : random_seed
-    use stdlib_stats_distribution_expon, only :                                 &
-        exp_pdf => exponential_distribution_pdf,                                &
-        rexp => exponential_distribution_rvs
+    use stdlib_stats_distribution_exponential, only:                            &
+                                 exp_pdf => exponential_distribution_pdf,       &
+                                 rexp => exponential_distribution_rvs
 
     implicit none
     real :: x(2,3,4),a(2,3,4)
-    complx :: scale
+    complex :: scale
     integer :: seed_put, seed_get
 
     seed_put = 1234567
@@ -143,15 +141,16 @@ program demo_exponential_pdf
     a(:,:,:) = 0.5
     print *, exp_pdf(x, a)     ! a rank 3 standard expon probability density
 
-! [0.457115263, 0.451488823, 0.492391467, 0.485233188, 0.446215510,
-!  0.401670188, 0.485127628, 0.316924453, 0.418474048, 0.483173639,
-!  0.307366133, 0.285812140, 0.448017836, 0.426440030, 0.403896868,
-!  0.334653258, 0.410376132, 0.485370994, 0.333617479, 0.263791025,
-!  0.249779820, 0.457159877, 0.495636940, 0.482243657]
+!  0.457115263  0.451488823  0.492391467  0.485233188  0.446215510 
+!  0.401670188  0.485127628  0.316924453  0.418474048  0.483173639 
+!  0.307366133  0.285812140  0.448017836  0.426440030  0.403896868 
+!  0.334653258  0.410376132  0.485370994  0.333617479  0.263791025 
+!  0.249779820  0.457159877  0.495636940  0.482243657
 
     scale = (1.0, 2.)
     print *, exp_pdf((1.5,1.0), scale)
-    ! a complex expon probability density function at (1.5,1.0) with real part of lamda=1.0 and imaginary part of lamda=2.0
+    ! a complex expon probability density function at (1.5,1.0) with real part
+    !of lamda=1.0 and imaginary part of lamda=2.0
 
 ! 6.03947677E-02
 
@@ -170,17 +169,16 @@ Cumulative distribution function of the exponential continuous distribution
 
 $$ F(x)=\begin{cases}1 - e^{-lamda \times x} &x\geqslant 0 \\\\ 0 &x< 0\end{} $$
 
-x is supported on [0, \infty)
 
 ### Syntax
 
-`result = [[stdlib_stats_distribution_expon(module):exponential_distribution_cdf(interface)]](x, lamda)`
+`result = [[stdlib_stats_distribution_exponential(module):exponential_distribution_cdf(interface)]](x, lamda)`
 
 ### Arguments
 
-`x`: has `intent(in)` and is a scalar of type `real` or `complx`.
+`x`: has `intent(in)` and is a scalar of type `real` or `complex`.
 
-`lamda`: has `intent(in)` and is a scalar of type `real` or `complx`.
+`lamda`: has `intent(in)` and is a scalar of type `real` or `complex`.
 
 The function is elemental, i.e., all auguments could be arrays conformable to each other. All arguments must have the same type.
 
@@ -193,13 +191,13 @@ The result is a scalar or an array, with a shape conformable to auguments, of ty
 ```fortran
 program demo_exponential_cdf
     use stdlib_stats_distribution_PRNG, only : random_seed
-    use stdlib_stats_distribution_expon, only :                                 &
+    use stdlib_stats_distribution_exponential, only :                           &
         exp_cdf => exponential_distribution_cdf,                                &
         rexp => exponential_distribution_rvs
 
     implicit none
     real :: x(2,3,4),a(2,3,4)
-    complx :: scale
+    complex :: scale
     integer :: seed_put, seed_get
 
     seed_put = 1234567
@@ -218,15 +216,16 @@ program demo_exponential_cdf
     a(:,:,:) = 0.5
     print *, exp_cdf(x, a)  ! a rank 3 array of standard exponential cumulative
 
-! [8.57694745E-02, 9.70223546E-02, 1.52170658E-02, 2.95336246E-02,
-!  0.107568979, 0.196659625, 2.97447443E-02, 0.366151094, 0.163051903,
-!  3.36527228E-02, 0.385267735, 0.428375721, 0.103964329, 0.147119939,
-!  0.192206264, 0.330693483, 0.179247737, 2.92580128E-02, 0.332765043,
-!  0.472417951, 0.500440359, 8.56802464E-02, 8.72612000E-03, 3.55126858E-02]
+!  8.57694745E-02  9.70223546E-02  1.52170658E-02  2.95336246E-02 
+!  0.107568979  0.196659625  2.97447443E-02  0.366151094  0.163051903 
+!  3.36527228E-02  0.385267735  0.428375721  0.103964329  0.147119939 
+!  0.192206264  0.330693483  0.179247737  2.92580128E-02  0.332765043 
+!  0.472417951  0.500440359  8.56802464E-02  8.72612000E-03  3.55126858E-02
 
     scale = (0.5,1.0)
     print *, exp_cdf((0.5,0.5),scale)
-    !complex exponential cumulative distribution at (0.5,0.5) with real part of lamda=0.5 and imaginary part of lamda=1.0
+    !complex exponential cumulative distribution at (0.5,0.5) with real part of
+    !lamda=0.5 and imaginary part of lamda=1.0
 
 ! 8.70351046E-02