Add files via upload

doc/specs/stdlib_stats_distribution_uniform.md

@@ -2,7 +2,7 @@
 title: stats_distribution
 ---
 
-# Statistical Distributions -- Uniform Distribution Module
+# Statistical Distributions Uniform Module
 
 [TOC]
 
@@ -22,7 +22,7 @@ Applying Fisher-Yates algorithm to generate an unbiased permutation for any list
 
 ### Arguments
 
-`list`: argument has `intent(in)` and is a rank one array of integer, real, or complex type.
+`list`: argument has `intent(in)` and is a rank one array of `integer`, `real`, or `complex` type.
 
 ### Return value
 
@@ -47,13 +47,19 @@ program demo_shuffle
  end do
  seed_put = 32165498
  call random_seed(seed_put, seed_get) ! set and get current value of seed
- n = shuffle(n) ! get randomized n
-![10, 6, 9, 2, 8, 1, 3, 5, 7, 4]
- x = shuffle(x) ! get randomized x
-! [5.0, 10.0, 9.0, 4.0, 3.0, 8.0, 2.0, 1.0, 7.0, 6.0]
- z = shuffle(z) ! get randomized z
-![(8.0, 8.0), (7.0, 7.0), (4.0, 4.0), (1.0, 1.0), (5.0, 5.0), (9.0, 9.0),
-!(6.0, 6.0), (3.0, 3.0), (2.0, 2.0), (10.0, 10.0)]
+ print *, shuffle(n) ! get randomized n
+
+!10 6 9 2 8 1 3 5 7 4
+
+ print *, shuffle(x) ! get randomized x
+
+!5.0 10.0 9.0 4.0 3.0 8.0 2.0 1.0 7.0 6.0
+
+ print *, shuffle(z) ! get randomized z
+
+!(8.0, 8.0) (7.0, 7.0) (4.0, 4.0) (1.0, 1.0) (5.0, 5.0)
+!(9.0, 9.0) (6.0, 6.0) (3.0, 3.0) (2.0, 2.0) (10.0, 10.0)
+
 end program demo_shuffle
 ```
 
@@ -65,35 +71,33 @@ Experimental
 
 ### Description
 
-Without augument the function returns a scalar standard uniformly distributed variate U(0,1) of real type with single precision on [0,1].
-
-With single augument `scale` of integer type the function returns a scalar uniformly distributed variate of integer type on [0,scale]. This is the standard Rectangular distribution. The function is elemental.
+Without augument the function returns a scalar standard uniformly distributed variate U(0,1) of `real` type with single precision on [0,1].
 
-With single augument `scale` of real or complex type the function returns a scalar uniformly distributed variate of real or complex type on [0, scale]. The real part and imaginary part of a complex type are independent of each other. Function is elemental.
+With single augument `scale` of `integer` type the function returns a scalar uniformly distributed variate of `integer` type on [0,scale]. This is the standard Rectangular distribtuion. Function is elemental.
 
-With double auguments `loc` and `scale` the function returns a scalar uniformly distributed random variates of integer, real or complx type on [loc, loc + scale] dependent of input type. If it is complex augument, the real part and imaginary part are independent of each other. Function is elemental.
+With single augument `scale` of `real` or `complex` type the function returns a scalar uniformly distributed variate of `real` or `complex` type on [0, scale]. The real part and imaginary part of a `complex` type are independent of each other. Function is elemental.
 
-With triple auguments `loc`, `scale` and `array_size` the function returns a rank one array of uniformly distributed variates of integer, real or complx type with an array size of `array_size`.
+With double auguments `loc` and `scale` the function returns a scalar uniformly distributed random variates of `integer`, `real` or `complex` type on [loc, loc + scale] dependent of input type. If it is `complex` augument, the real part and imaginary part are independent of each other. Function is elemental.
 
-`scale` must be greater than 0.
+With triple auguments `loc`, `scale` and `array_size` the function returns a rank one array of uniformly distributed variates of `integer`, `real` or `complex` type with an array size of `array_size`.
 
 ### Syntax
 
 `result = [[stdlib_stats_distribution_uniform(module):uniform_distribution_rvs(interface)]]([[loc,] scale] [[[,array_size]]])`
 
 ### Arguments
 
-`loc`: optional argument has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`loc`: optional argument has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
-`scale`: optional argument has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`scale`: optional argument has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
 `array_size`: optional argument has `intent(in)` and is a scalar of type `integer`.
 
 `loc` and `scale` must have the same type when both are present.
 
 ### Return value
 
-The result is a scalar or a rank one array, with size of `array_size`, of type `integer`, `real` or `complx` depending on the input type.
+The result is a scalar or a rank one array, with size of `array_size`, of type `integer`, `real` or `complex` depending on the input type.
 
 ### Example
 
@@ -103,7 +107,7 @@ program demo_uniform_rvs
  use stdlib_stats_distribution_uniform, only:uni=> uniform_distribution_rvs
 
  implicit none
- complx :: loc, scale
+ complex :: loc, scale
  real :: a(3,4,5), b(3,4,5)
  integer :: seed_put, seed_get
 
@@ -119,8 +123,10 @@ program demo_uniform_rvs
  print *, uni(-0.5, 1.0) !an uniform random variate in [-0.5, 0.5]
 ! 0.486900032
 
- print *, uni(-1.0,2.0,10) !an array of 10 uniform random variates in [-1., 1.]
-![0.884182811, -0.771520197, 0.560377002, 0.709313750, -7.12267756E-02, -0.431066573, 0.497536063, -0.396331906, -0.325983286, 0.137686729]
+ print *, uni(-1.0,2.0,10) 
+ !an array of 10 uniform random variates in [-1., 1.]
+
+!0.884182811 -0.771520197 0.560377002 0.709313750 -7.12267756E-02 !-0.431066573 0.497536063 -0.396331906 -0.325983286 0.137686729
 
  print *, uni(20) !a random integer variate in [0, 20]
 ! 17
@@ -129,50 +135,54 @@ program demo_uniform_rvs
 ! 15
 
  print *, uni(3,19,10) !an array of 10 integer variates in [3,22]
-! [7, 16, 16, 12, 9, 21, 19, 4, 3, 19]
+
+!7 16 16 12 9 21 19 4 3 19
 
  loc = (-0.5, -0.5)
  scale = (1.0, 1.0)
 
  print *, uni(scale) !a complex uniform random variate in unit square
-!(0.139202669,0.361759573)
+
+!(0.139202669, 0.361759573)
 
  print *, uni(loc,scale)
  !a complex uniform random variate in [(-0.5, -0.5), (0.5, 0.5)]
+
 !(0.296536088,-0.143987954)
 
  print *, uni(loc, scale, 10)
  !an array of 10 complex uniform random variate in [(-0.5, -0.5), (0.5, 0.5)]
 
-![(-0.302334785,-0.401923567), (0.281620383,9.534919262E-02),
-! (-0.374348879,0.457528770), (0.442990601,-0.240510434),
-! (-0.421572685,0.279313922), (-0.182090610,5.901372433E-02),
-! (-7.864198089E-02,0.378484428), (-0.423258364,-0.201292425),
-! (0.193327367,-0.353985727), (-0.397661150,0.355926156)]
+!(-0.302334785,-0.401923567) (0.281620383,9.534919262E-02)
+! (-0.374348879,0.457528770) (0.442990601,-0.240510434)
+! (-0.421572685,0.279313922) (-0.182090610,5.901372433E-02)
+! (-7.864198089E-02,0.378484428) (-0.423258364,-0.201292425)
+! (0.193327367,-0.353985727) (-0.397661150,0.355926156)
 
  a(:,:,:) = -0.5
  b(:,:,:) = 1.0
 
  print *, uni(a,b)
  !a rank 3 array of random variates in [-0.5,0.5]
 
-! [-0.249188632, -0.199248433, -0.389813602, 2.88307667E-03, 0.238479793,
-! 0.264856219, -0.205177426, -0.480921626, 0.131218433, 0.252170086,
-! -0.303151041, -8.89462233E-02, -0.377370685, 0.341802299, 0.323204756,
-! 0.358679056, -0.138909757, 0.384329498, -0.109372199, 0.132353067,
-! 0.494320452, 0.419343710, -0.103044361, 0.461389005, 0.403132677,
-! 0.121850729, 0.403839290, -0.349389791, 0.490482628, 0.156600773,
-! 8.46788883E-02, -0.483680278, 0.388107836, 0.119698405, 0.154214382,
-! 0.153113484, 0.236523747, 0.155937552, -0.135760903, 0.219589531,
-! 0.394639254, 6.30156994E-02, -0.342692465, -0.444846451, -0.215700030,
-! 0.204189956, -0.208748132, 0.355063021, 8.98272395E-02, -0.237928331,
-! 2.98077464E-02, -0.485149682, -8.06870461E-02, -0.372713923,
-! -0.178335011, 0.283877611, -2.13934183E-02, -9.21690464E-03, 4.56320047E-02,
-! 0.220112979]
+! -0.249188632 -0.199248433 -0.389813602 2.88307667E-03 0.238479793,
+! 0.264856219 -0.205177426 -0.480921626 0.131218433 0.252170086,
+! -0.303151041 -8.89462233E-02 -0.377370685 0.341802299 0.323204756,
+! 0.358679056 -0.138909757 0.384329498 -0.109372199 0.132353067,
+! 0.494320452 0.419343710 -0.103044361 0.461389005 0.403132677
+! 0.121850729 0.403839290 -0.349389791 0.490482628 0.156600773
+! 8.46788883E-02 -0.483680278 0.388107836 0.119698405 0.154214382
+! 0.153113484 0.236523747 0.155937552 -0.135760903 0.219589531
+! 0.394639254 6.30156994E-02 -0.342692465 -0.444846451 -0.215700030
+! 0.204189956 -0.208748132 0.355063021 8.98272395E-02 -0.237928331
+! 2.98077464E-02 -0.485149682 -8.06870461E-02 -0.372713923
+! -0.178335011 0.283877611 -2.13934183E-02 -9.21690464E-03
+! 4.56320047E-02 0.220112979
+
 end program demo_uniform_rvs
 ```
 
-## `uniform_distribution_pdf` - uniform probability density function
+## `uniform_distribution_pdf` - Uniform probability density function
 
 ### Status
 
@@ -184,19 +194,19 @@ The probability density function of the uniform distribution.
 
 f(x) = 1 / (scale + 1); for discrete uniform distribution
 f(x) = 1 / scale; for continuous uniform distribution
-f(x) = 1 / (scale%re * scale%im); for complx uniform distribution
+f(x) = 1 / (scale%re * scale%im); for complex uniform distribution
 
 ### Syntax
 
 `result = [[stdlib_stats_distribution_uniform(module):uniform_distribution_pdf(interface)]](x, loc, scale)`
 
 ### Arguments
 
-`x`: has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`x`: has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
-`loc`: has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`loc`: has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
-`scale`: has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`scale`: has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
 The function is elemental, i.e., all three auguments could be arrays conformable to each other. All three arguments must have the same type.
 
@@ -214,7 +224,7 @@ program demo_uniform_pdf
  uni => uniform_distribution_rvs
 
  implicit none
- complx :: loc, scale
+ complex :: loc, scale
  real :: a(3,4,5), b(3,4,5), x(3,4,5)
  integer :: seed_put, seed_get
 
@@ -239,16 +249,16 @@ program demo_uniform_pdf
  x = reshape(uni(0.,2.,60),[3,4,5])! uniform random variates array in [0., 2.]
  print *, uni_pdf(x, a, b) ! probability density array in [0., 2.]
 
-![0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, &
-! 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000, 0.500000000]
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000  &
+! 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000 0.500000000
 
  loc = (-0.5,-0.5)
  scale = (1.0,1.0)
@@ -260,7 +270,7 @@ end program demo_uniform_pdf
 
 ```
 
-## `uniform_distribution_cdf` - uniform cumulative distribution function
+## `uniform_distribution_cdf` - Uniform cumulative distribution function
 
 ### Status
 
@@ -272,19 +282,19 @@ Cumulative distribution function of the uniform distribution
 
 F(x) = (x - loc + 1) / (scale + 1); for discrete uniform distribution
 F(x) = (x - loc) / scale; for continuous uniform distribution
-F(x) = (x%re - loc%re)(x%im - loc%im) / (scale%re * scale%im); for complx uniform distribution
+F(x) = (x%re - loc%re)(x%im - loc%im) / (scale%re * scale%im); for complex uniform distribution
 
 ### Syntax
 
 `result = [[stdlib_stats_distribution_uniform(module):uniform_distribution_cdf(interface)]](x, loc, scale)`
 
 ### Arguments
 
-`x`: has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`x`: has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
-`loc`: has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`loc`: has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
-`scale`: has `intent(in)` and is a scalar of type `integer`, `real` or `complx`.
+`scale`: has `intent(in)` and is a scalar of type `integer`, `real` or `complex`.
 
 The function is elemental, i.e., all three auguments could be arrays conformable to each other. All three arguments must have the same type.
 
@@ -296,12 +306,14 @@ The result is a scalar or an array, with a shape conformable to auguments, of ty
 
 ```fortran
 program demo_uniform_cdf
- use stdlib_stats_distribution_uniform, only : uni_cdf => uniform_distribution_cdf, &
- uni => uniform_distribution_rvs, &
  use stdlib_stats_distribution_PRNG, only : random_seed
+ use stdlib_stats_distribution_uniform, only : &
+ uni_cdf => uniform_distribution_cdf, &
+ uni => uniform_distribution_rvs, &
+
  implicit none
  real :: x(3,4,5), a(3,4,5), b(3,4,5)
- complx :: loc, scale
+ complex :: loc, scale
  integer :: seed_put, seed_get
 
  seed_put = 1234567
@@ -324,16 +336,16 @@ program demo_uniform_cdf
  x = reshape(uni(-1.0,2.0,60),[3,4,5]) ! uniform random variates array
  print *, uni_cdf(x,a,b) ! cumulative array in [-1.0, 1.0]
 
-![0.161520004, 0.553248405, 0.986900032, 0.942091405, 0.114239901, 0.780188501, &
-! 0.854656875, 0.464386612, 0.284466714, 0.748768032, 0.301834047, 0.337008357, &
-!0.568843365, 0.596165061, 0.180993259, 0.614166319, 0.214835495,7.98164606E-02,&
-!0.641274095, 0.607101977, 0.701139212, 0.230517209, 1.97925568E-02,0.857982159,&
-!0.712761045, 0.139202654, 0.361759573, 0.796536088, 0.356012046, 0.197665215, &
-!9.80764329E-02,0.781620383, 0.595349193, 0.125651121, 0.957528770, 0.942990601,&
-!0.259489566, 7.84273148E-02, 0.779313922, 0.317909390, 0.559013724,0.421358019,&
-!0.878484428, 7.67416358E-02, 0.298707575, 0.693327367, 0.146014273,0.102338850,&
-!0.855926156, 0.250811368, 0.300751567, 0.110186398, 0.502883077, 0.738479793, &
-!0.764856219, 0.294822574, 1.90783739E-02,0.631218433,0.752170086, 0.196848959]
+!0.161520004 0.553248405 0.986900032 0.942091405 0.114239901 0.780188501  &
+! 0.854656875 0.464386612 0.284466714 0.748768032 0.301834047 0.337008357  &
+!0.568843365 0.596165061 0.180993259 0.614166319 0.214835495 7.98164606E-02 &
+!0.641274095 0.607101977 0.701139212 0.230517209 1.97925568E-02 0.857982159 &
+!0.712761045 0.139202654 0.361759573 0.796536088 0.356012046 0.197665215  &
+!9.80764329E-02 0.781620383 0.595349193 0.125651121 0.957528770 0.942990601 &
+!0.259489566 7.84273148E-02 0.779313922 0.317909390 0.559013724 0.421358019 &
+!0.878484428 7.67416358E-02 0.298707575 0.693327367 0.146014273 0.102338850 &
+!0.855926156 0.250811368 0.300751567 0.110186398 0.502883077 0.738479793  &
+!0.764856219 0.294822574 1.90783739E-02 0.631218433 0.752170086 0.196848959
 
  loc = (0., 0.)
  scale=(2., 1.)