migrate

Change architecture

Upgrade crystal version

Change license to GPL-3

Add several new functions and helpers (radian/degree, means, macd, ...)

CHANGELOG.md

@@ -1,30 +0,0 @@
-# v0.1.6
-- Improve factorial (handle BigInt)
-- Improve distributions (handle BigFloat and BigInt)
-- Define more specs
-- Improve Normale Distribution parameters (min-max instead of a-b)
-
-# v0.1.5
-- add specs for every function
-- improve file architecture
-
-# v0.1.4
-- fix binomial distribution
-
-# v0.1.3
-- renamed crystal_proba to stats
-
-# v0.1.2
-- renamed CrystalProba to crystal_proba
-
-# v0.1.0
-
-## Added
-- Initialization of the project
-- The Binomial Distribution and Normale Distribution are added
-- Basic specs are provided as documentation and unitary tests
-- License set to MIT
-- Compatibility with crystal v0.18
-
-## Notes
-- Project inherited from RubyBinomial and RubyNormale, from myself

LICENSE

@@ -1,21 +1,674 @@
-The MIT License (MIT)
+                    GNU GENERAL PUBLIC LICENSE
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+  The Free Software Foundation may publish revised and/or new versions of
+the GNU General Public License from time to time.  Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+  Each version is given a distinguishing version number.  If the
+Program specifies that a certain numbered version of the GNU General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation.  If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+  If the Program specifies that a proxy can decide which future
+versions of the GNU General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+  15. Disclaimer of Warranty.
+
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
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+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    {one line to give the program's name and a brief idea of what it does.}
+    Copyright (C) {year}  {name of author}
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    {project}  Copyright (C) {year}  {fullname}
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

README.md

@@ -1,7 +1,9 @@
+**Migrated to <https://git.sceptique.eu/Sceptique/stats>**
+
 # stats
 
 An expressive implementation of statistical distributions.
-Compatible with crystal v0.18
+Compatible with crystal v0.27.0.
 
 ## Installation
 
@@ -9,30 +11,131 @@ Add this to your application's `shard.yml`:
 
 ```yaml
 dependencies:
-  Stats:
-    github: Nephos/stats
+  stats:
+    git: https://git.sceptique.eu/Sceptique/stats
 ```
 
 
 ## Usage
 
+### Include it
+
 ```crystal
 require "stats"
+include Stats
 ```
 
-You should read the specs to understand how it works.
+### Normal distribution
+
 ```crystal
-NormaleDistribution::between standard_deviation: 15, esperance: 100, min: 85, max: 115 # => 0.6826894921370859
-Math.binomial_distribution(tries: 3, probability: 0.5, success: 1) # => 0.375
+NormaleDistribution.between # less_than, greater_than
+  standard_deviation: 15,
+  esperance: 100,
+  min: 85,
+  max: 115
+  # => 0.6826894921370859
+```
+
+### Binomial distribution
+
+```crystal
+Math.binomial_distribution(
+  tries: 3,
+  probability: 0.5,
+  success: 1)
+  # => 0.375
+```
+
+### Binomial coefficient
+
+```crystal
+Math.coef_binomial(5, 2) # => 10
+```
+
+### Factorial
+
+```crystal
+Math.factorial(4) # => 24
+```
+
+### Radian and degree
+
+```crystal
+90.radian # => (Math::PI / 2)
+(Math::PI / 4) # => 45.0
+```
+
+### Series & Statistics
+
+```crystal
+[1, 2, 3].mean # => 2.0
+[1, 2, 3].variance # => 0.6667
+[1, 2, 3].standard_deviation # => 0.8165
+[1, 2, 3].quadratic_mean # => 2.16
+[2, 32].geometric_mean # => 8.0
+[40, 60].harmonic_mean # => 48.0
+[1,2,3,2,1].macd 3 # => [2.0, 2.333, 2.0]
+```
+
+### Correlations
+
+```crystal
+[1,2,3,4].covariance [4,2,1,0] # => -1.625
+[1,2,3,4].correlation_coef [1,2,3,3] + 1 > 1.5 # => true
+[1,2,3,4].correlation_coef [-14,14,101,-100] + 1 > 1.5 # => false
+```
+
+### Median
+
+```crystal
+[1, 2, 5].median # => 2.0
+[42, 1337].median # => 685.5
+```
+
+### Quartiles & Boxplot
+
+*Note: not big compatible yet*
+
+```crystal
+[1, 3, 5].first_quartile  # => 2.0 (alias of lower_quartile)
+[1, 3, 5].second_quartile # => 3.0 (alias of median)
+[1, 3, 5].third_quartile  # => 4.0 (alias of upper_quartile)
+[1, 3, 5].quartiles       # => [2.0, 3.0, 4.0] ([Q1, Q2, Q3])
+```
+
+```crystal
+arr = [-23, -5, 2, 5, 5, 6, 7, 8, 14, 15, 42, 1337]
+
+arr.first_quartile  # => 3.5  (Q1)
+arr.second_quartile # => 6.5  (Q2)
+arr.third_quartile  # => 14.5 (Q3)
+arr.interquartile_range # => 11.0 (alias of iqr) (IQR = Q3 - Q1)
+
+# Tukey's fences with k = 1.5 (default parameter value)
+arr.lower_fence # => -13.0 (Q1 - 1.5 * IQR)
+arr.upper_fence # => 31    (Q3 + 1.5 * IQR)
+arr.lower_outliers # => [-23]
+arr.upper_outliers # => [42, 1337]
+
+# Tukey's fences with k = 3 for "far out" outliers
+arr.upper_fence(3)    # => 47.5 (Q3 + 3 * IQR)
+arr.upper_outliers(3) # => [1337]
+```
+
+### Frequency
+
+```crystal
+[0, 1, 2, 3].frequency_of(0) # => 0.25 (amount of X in the population, by the size of the population)
+[0, 0, 1, 2, 3].all_frequencies # => { 0 => 0.4, 1 => 0.2, 2 => 0.2, 3 => 0.2}
 ```
 
 ## Development
 
-- The lib is adapted to be usable with BigInt and BigFloat values
+- The lib should take care of "big" numbers
 
 ## Contributing
 
-1. Fork it ( https://github.com/Nephos/crystal_proba/fork )
+1. Fork it ( https://github.com/Nephos/stats/fork )
 2. Create your feature branch (git checkout -b my-new-feature)
 3. Commit your changes (git commit -am 'Add some feature')
 4. Push to the branch (git push origin my-new-feature)

shard.yml

@@ -1,7 +1,7 @@
 name: stats
-version: 0.1.6
+version: 0.3.0
 
 authors:
   - Arthur Poulet <arthur.poulet@mailoo.org>
 
-license: MIT
+license: GPL-3.0

spec/binomial_distribution.cr

@@ -1,35 +1,34 @@
-describe Math do
+include Stats
 
+describe Math do
   it "binomial_distribution" do
-    0.0.step(by: 0.1, limit: 1.0) do |proba|
+    0.0.step(by: 0.1, to: 1.0) do |proba|
       Math.binomial_distribution(tries: 1, probability: proba, success: 1).should eq(proba)
     end
     Math.binomial_distribution(tries: 10, probability: 0.2, success: 3).round(3).should eq(0.201)
     Math.binomial_distribution(tries: 10, probability: 0.2, success: 6).round(4).should eq(0.0055)
   end
-
 end
 
 describe BinomialDistribution do
-
   it "initialize" do
-    BinomialDistribution.new(0).should be_a(BinomialDistribution)
-    BinomialDistribution.new(1).should be_a(BinomialDistribution)
-    BinomialDistribution.new(100).should be_a(BinomialDistribution)
-    BinomialDistribution.new(1, 0).should be_a(BinomialDistribution)
-    BinomialDistribution.new(1, 0.5).should be_a(BinomialDistribution)
-    BinomialDistribution.new(1, 1).should be_a(BinomialDistribution)
+    BinomialDistribution(Int32, Float64).new(0).should be_a(BinomialDistribution(Int32, Float64))
+    BinomialDistribution(Int32, Float64).new(1).should be_a(BinomialDistribution(Int32, Float64))
+    BinomialDistribution(Int32, Float64).new(100).should be_a(BinomialDistribution(Int32, Float64))
+    BinomialDistribution(Int32, Int32).new(1, 0).should be_a(BinomialDistribution(Int32, Int32))
+    BinomialDistribution.new(1, 0.5).should be_a(BinomialDistribution(Int32, Float64))
+    BinomialDistribution.new(1, 1).should be_a(BinomialDistribution(Int32, Int32))
   end
 
   it "initialize errors" do
-    expect_raises { BinomialDistribution.new(-1) }
-    expect_raises { BinomialDistribution.new(0, -1) }
-    expect_raises { BinomialDistribution.new(0, 1.5) }
+    expect_raises(Math::DomainError) { BinomialDistribution(Int32, Float64).new(-1) }
+    expect_raises(Math::DomainError) { BinomialDistribution.new(0, -1) }
+    expect_raises(Math::DomainError) { BinomialDistribution.new(0, 1.5) }
   end
 
   it "distribute" do
     b = BinomialDistribution.new(2, 0.5)
-    b.should be_a(BinomialDistribution)
+    b.should be_a(BinomialDistribution(Int32, Float64))
     b.distribute(0).should eq 0.25
     b.distribute(1).should eq 0.5
     b.distribute(2).should eq 0.25
@@ -38,9 +37,16 @@ describe BinomialDistribution do
     b.distribute([2, 1]).should eq 0.75
   end
 
-  it "with BitNumber" do
-    BinomialDistribution.new(
-      BigInt.new(1), BigFloat.new(1)).should be_a(BinomialDistribution)
+  it "with spaces tests" do
   end
 
+  it "with BitNumber" do
+    BinomialDistribution.new(BigInt.new(1), BigFloat.new(1)).should be_a(BinomialDistribution(BigInt, BigFloat))
+    ((a = BinomialDistribution.new(BigInt.new(10), BigFloat.new(0.02)).distribute(BigInt.new(1)..BigInt.new(10))) > 0.02).should be_true
+    ((b = BinomialDistribution.new(BigInt.new(20), BigFloat.new(0.02)).distribute(BigInt.new(1)..BigInt.new(20))) > 0.02).should be_true
+    ((c = BinomialDistribution.new(BigInt.new(50), BigFloat.new(0.02)).distribute(BigInt.new(1)..BigInt.new(50))) > 0.02).should be_true
+    (b > a).should be_true
+    (c > b).should be_true
+    # p a, b, c
+  end
 end

spec/math/angle.cr

@@ -0,0 +1,15 @@
+describe Math::Angle do
+  it "verify radian to degree" do
+    45.radian.should eq(Math::PI / 4)
+    90.radian.should eq(Math::PI / 2)
+    180.radian.should eq(Math::PI)
+    360.radian.should eq(Math::PI * 2)
+  end
+
+  it "verify degree to radian" do
+    (Math::PI / 4).degree.should eq(45)
+    (Math::PI / 2).degree.should eq(90)
+    (Math::PI).degree.should eq(180)
+    (Math::PI * 2).degree.should eq(360)
+  end
+end

spec/math/coef_binomial.cr

@@ -12,11 +12,11 @@ describe Math do
     Math.coef_binomial(261, 262).should eq 0
     Math.coef_binomial(261, 263).should eq 0
     Math.coef_binomial(261, 26372).should eq 0
-    20.times {|i| Math.coef_binomial(i + 1, i + rand(1..5) + 1).should eq 0}
+    20.times { |i| Math.coef_binomial(i + 1, i + rand(1..5) + 1).should eq 0 }
   end
 
   it "coef binomial tests a = b" do
-    20.times {|i| Math.coef_binomial(i + 1, i + 1).should eq 1}
+    20.times { |i| Math.coef_binomial(i + 1, i + 1).should eq 1 }
   end
 
   it "coef_binomial with BigInt" do
@@ -25,5 +25,4 @@ describe Math do
       BigInt.new("fffffffffffffffffffffffffffffffe", 16),
       BigInt.new("ffffffffffffffffffffffffffffffff", 16)).should eq 0
   end
-
 end

spec/math/correlation.cr

@@ -0,0 +1,21 @@
+require "big"
+
+describe Math::Correlation do
+  it "test basic confidence interval" do
+    arr1 = [1, 2, 2.5, 3, 3.5, 3.8, 4, 4.2, 4.4, 4.5]
+    arr2 = [1, 2, 3, 4, 5, 6.5, 8, 10, 12, 15]
+    arr1.mean.round(4).should eq 3.29
+    arr2.mean.round(4).should eq 6.65
+    arr1.size.should eq 10
+    arr2.size.should eq 10
+    arr1.covariance(arr2).round(4).should eq 4.2215
+    arr1.correlation_coef(arr2).round(4).should eq 0.8906
+  end
+
+  it "test big" do
+    [BigInt.new(1), 2].correlation_coef([2, 3])
+    [1, 2].correlation_coef([BigInt.new(2), 3])
+    [BigInt.new(1), 2].correlation_coef([BigInt.new(2), 3])
+    [1, 2].correlation_coef([BigInt.new(2), BigInt.new(3)])
+  end
+end

spec/math/factorial.cr

@@ -1,5 +1,4 @@
 describe Math do
-
   it "factorial" do
     Math.factorial(0).should eq 1
     Math.factorial(1).should eq 1
@@ -11,9 +10,8 @@ describe Math do
     Math.factorial(6).should eq 720
   end
 
-  it "factorial bigint" do
-    res = (1..20).to_a.reduce(BigInt.new 1) {|e, i| e * BigInt.new(i) }
-    Math.factorial(BigInt.new 20).should eq res
+  it "factorial big" do
+    res = (1..20).to_a.reduce(BigInt.new(1)) { |e, i| e * BigInt.new(i) }
+    Math.factorial(BigInt.new(20)).should eq res
   end
-
 end

spec/math/frequency.cr

@@ -0,0 +1,34 @@
+FREQ_LIMIT = 100
+
+describe Math::Frequency do
+  it "test trivia" do
+    ([] of Int32).frequency_of(0).should eq 0.0
+    [0, 1, 2, 3].frequency_of(0).should eq 0.25
+    [0, 0, 1, 2, 3].frequency_of(0).should eq 0.40
+    [0, 0, 1, 2, 3].all_frequencies.should eq({0 => 0.4, 1 => 0.2, 2 => 0.2, 3 => 0.2})
+    # allfreq1 = [0, 0, 1, 2, 3].all_frequencies(2)
+    # allfreq1[1].should eq 0.4
+    # allfreq1.size.should eq 2
+    # expect_raises(Error) { [0, 0, 1, 2, 3].all_frequencies(2, true) }
+  end
+
+  it "test basic" do
+    FREQ_LIMIT.times do |modi|
+      modulo = modi + 1
+      # we should have the same or more because we don't / modulo in the freq
+      arr = FREQ_LIMIT.times.to_a.map { |e| e % modulo }
+      (arr.frequency_of(0) >= (1.0f64 / modulo)).should be_true
+
+      next if modulo <= 20
+      # make an array with less or equal amount of iterations
+      arr_less = FREQ_LIMIT.times.to_a.map { |e| e % (modulo + 5) }
+      (arr.frequency_of(0) >= arr_less.frequency_of(0)).should be_true
+
+      # make an array with more or equal amount of iterations
+      arr_more = FREQ_LIMIT.times.to_a.map { |e| e % (modulo - 5) }
+      (arr.frequency_of(0) <= arr_more.frequency_of(0)).should be_true
+    end
+
+    [0, 0, 0, 0, 1, 1, 1, 2, 2, 3].all_frequencies.should eq({0 => 0.4, 1 => 0.3, 2 => 0.2, 3 => 0.1})
+  end
+end

spec/math/macd.cr

@@ -0,0 +1,11 @@
+require "big"
+
+describe Math::MACD do
+  it "test basic macd" do
+    [1, 2, 3, 2, 1].macd(3).map { |e| e.round(3) }.should eq [2, 2.333, 2]
+  end
+
+  it "test big basic macd" do
+    puts [BigInt.new(1), BigInt.new(2), BigInt.new(3), BigInt.new(2), 1].macd(3).map { |e| e.round(3) }.should eq [2, 2.333, 2]
+  end
+end

spec/math/mean.cr

@@ -0,0 +1,43 @@
+require "big"
+
+describe Math::Mean do
+  it "test several basic mean special case" do
+    arr = ([] of Int32)
+    arr.mean.should eq 0.0
+    arr.quadratic_mean.should eq 0.0
+    arr.harmonic_mean.should eq 0.0
+    arr.geometric_mean.should eq 0.0
+  end
+
+  it "test mean on Array(Float64)" do
+    [1.0, 2.0, 3.0].mean.should eq 2.0
+    [1.0, 2.0, -3.0].mean.should eq 0.0
+  end
+
+  it "test mean on Array(Int32)" do
+    [1, 2, 3].mean.should eq 2.0
+    [1, 2, -3].mean.should eq 0.0
+  end
+
+  it "test mean on big" do
+    [BigInt.new(1), 2, 3].mean.should eq 2.0
+    [BigInt.new(1), BigInt.new(2), BigFloat.new(-3)].mean.should eq 0.0
+  end
+
+  it "test quadratic mean" do
+    [1, 2, 3, 2].quadratic_mean.round(4).should eq(2.1213)
+    [1, 2, 1, 5, 10, 9, 1, -13, 2].quadratic_mean.round(4).should eq(6.549)
+  end
+
+  it "test geometric mean" do
+    [2, 32].geometric_mean.should eq(8)
+    [10, 15].geometric_mean.round(2).should eq(12.25)
+    [5, 3, 12].geometric_mean.round(2).should eq(5.65)
+    [7, 9, 12].geometric_mean.round(2).should eq(9.11)
+  end
+
+  it "test harmonic mean" do
+    [1, 4, 1, 2].harmonic_mean.round(3).should eq(1.455)
+    [13, 23, 12, 44, 55].harmonic_mean.round(3).should eq(20.438)
+  end
+end

spec/math/median.cr

@@ -0,0 +1,23 @@
+require "big"
+
+describe Math::Median do
+  it "test trivia" do
+    arr = ([] of Int32)
+    arr.median.should eq 0.0
+  end
+
+  it "test basic" do
+    [1.0, 2.0].median.should eq 1.5
+    [42, 1337].median.should eq 689.5
+
+    [1, 2, 5].median.should eq 2.0
+    [2, 5, 1].median.should eq 2.0
+
+    [4, 1, 1, 1, 2].median.should eq 1.0
+  end
+
+  it "test big" do
+    [BigInt.new(1.0), 2.0].median.should eq 1.5
+    [BigInt.new(1.0), BigFloat.new(2.0)].median.should eq 1.5
+  end
+end

spec/math/quartile.cr

@@ -0,0 +1,98 @@
+require "big"
+
+module Math::Quartile
+  it "trivial" do
+    arr = [1, 3, 5]
+
+    arr.first_quartile.should eq 2.0
+    arr.second_quartile.should eq 3.0
+    arr.third_quartile.should eq 4.0
+
+    arr.quartiles.should eq [2.0, 3.0, 4.0]
+
+    arr.iqr.should eq 2.0
+  end
+
+  # TODO
+  # it "big" do
+  #   arr = [BigInt.new(1), BigFloat.new(3), 5]
+  #
+  #   arr.first_quartile.should eq 2.0
+  #   arr.second_quartile.should eq 3.0
+  #   arr.third_quartile.should eq 4.0
+  #
+  #   arr.quartiles.should eq [2.0, 3.0, 4.0]
+  #
+  #   arr.iqr.should eq 2.0
+  # end
+
+  it "odd size input" do
+    arr = [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49]
+
+    arr.first_quartile.should eq 25.5
+    arr.second_quartile.should eq 40
+    arr.third_quartile.should eq 42.5
+
+    arr.quartiles.should eq [25.5, 40, 42.5]
+
+    arr.iqr.should eq 17.0
+  end
+
+  it "even size input" do
+    arr = [7, 15, 36, 39, 40, 41]
+
+    arr.first_quartile.should eq 15.0
+    arr.second_quartile.should eq 37.5
+    arr.third_quartile.should eq 40.0
+
+    arr.quartiles.should eq [15, 37.5, 40]
+
+    arr.iqr.should eq 25.0
+  end
+
+  it "complex" do
+    arr = [7, 7, 31, 31, 47, 75, 87, 115, 116, 119, 119, 155, 177]
+
+    arr.first_quartile.should eq 31
+    arr.second_quartile.should eq 87
+    arr.third_quartile.should eq 119
+
+    arr.quartiles.should eq [31, 87, 119]
+
+    arr.iqr.should eq 88
+  end
+
+  it "complex 2" do
+    # https://en.wikipedia.org/wiki/Quartile#Example_1
+    arr = [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49]
+
+    arr.first_quartile.should eq 25.5
+    arr.second_quartile.should eq 40
+    arr.third_quartile.should eq 42.5
+
+    arr.quartiles.should eq [25.5, 40, 42.5]
+
+    arr.iqr.should eq 17
+  end
+
+  it "boxplot values" do
+    arr = [-23, -5, 2, 5, 5, 6, 7, 8, 14, 15, 42, 1337]
+
+    arr.first_quartile.should eq 3.5
+    arr.second_quartile.should eq 6.5
+    arr.third_quartile.should eq 14.5
+
+    arr.quartiles.should eq [3.5, 6.5, 14.5]
+
+    arr.iqr.should eq 11.0
+
+    arr.lower_fence.should eq -13.0
+    arr.upper_fence.should eq 31
+
+    arr.lower_outliers.should eq [-23]
+    arr.upper_outliers.should eq [42, 1337]
+
+    arr.upper_fence(3).should eq 47.5
+    arr.upper_outliers(3).should eq [1337]
+  end
+end

spec/math/standard_deviation.cr

@@ -0,0 +1,37 @@
+describe Math::StandardDeviation do
+  it "test variance & std dev explained" do
+    arr = [1, 2, 3, 4, 4]
+    mean = (4 + 4 + 3 + 2 + 1) / 5.0
+    variance = ((4 - mean)**2 + (4 - mean)**2 + (3 - mean)**2 + (2 - mean)**2 + (1 - mean)**2) / 5.0
+    standard_deviation = Math.sqrt(variance)
+    arr.mean.should eq(mean)
+    arr.variance.should eq(variance)
+    arr.standard_deviation.should eq(standard_deviation)
+  end
+
+  it "test big" do
+    arr = [BigInt.new(1), BigFloat.new(2), 3, 4.0, 4]
+    mean = (4 + 4 + 3 + 2 + 1) / 5.0
+    variance = ((4 - mean)**2 + (4 - mean)**2 + (3 - mean)**2 + (2 - mean)**2 + (1 - mean)**2) / 5.0
+    standard_deviation = Math.sqrt(variance)
+    arr.mean.should eq(mean)
+    arr.variance.should eq(variance)
+    arr.standard_deviation.should eq(standard_deviation)
+  end
+
+  it "test standard deviation without explanations" do
+    arr = [1, 5, 23, 2, 0, 0, 1]
+    arr.mean.round(2).should eq 4.57
+    arr.variance.round(2).should eq 59.10
+    arr.standard_deviation.round(2).should eq 7.69
+
+    [1.0, 2.0, 3.0].variance.round(4).should eq(0.6667)
+    [1.0, 2.0, 3.0].standard_deviation.round(4).should eq(0.8165)
+  end
+
+  it "test several special case" do
+    arr = [] of Int32
+    arr.variance.should eq 0.0
+    arr.standard_deviation.should eq 0.0
+  end
+end

spec/normale_distribution.cr

@@ -1,3 +1,5 @@
+include Stats
+
 describe NormaleDistribution do
   it "between" do
     bet = NormaleDistribution.between standard_deviation: 1, esperance: 0, min: -1, max: 1
@@ -8,11 +10,10 @@ describe NormaleDistribution do
 end
 
 describe NormaleDistribution::Persistant do
-
   it "instances" do
-    NormaleDistribution::Persistant.new
-    NormaleDistribution::Persistant.new(standard_deviation: 12).standard_deviation.should eq(12)
-    NormaleDistribution::Persistant.new(esperance: 14).esperance.should eq(14)
+    NormaleDistribution::Persistant(Float64, Float64).new
+    NormaleDistribution::Persistant(Int32, Float64).new(standard_deviation: 12).standard_deviation.should eq(12)
+    NormaleDistribution::Persistant(Float64, Int32).new(esperance: 14).esperance.should eq(14)
   end
 
   it "instances with BigNumber" do
@@ -29,8 +30,8 @@ describe NormaleDistribution::Persistant do
   end
 
   it "centroid" do
-    [0.1, 1, 2, 4.1324].each do |space|
-      [0, 1, -1, 12, 41, 0.2, 0.233].each do |center|
+    [0.1, 1.0, 2.0, 4.1324].each do |space|
+      [0.0, 1.0, -1.0, 12.0, 41.0, 0.2, 0.233].each do |center|
         rule = NormaleDistribution::Persistant.new standard_deviation: space, esperance: center
         [0.2, 0.4, 0.45, 0.55, 0.94, 1.1].each do |diff|
           (-rule.between(diff, center)).should eq(rule.between(center, diff))
@@ -40,8 +41,7 @@ describe NormaleDistribution::Persistant do
   end
 
   it "must fail" do
-    expect_raises { NormaleDistribution::Persistant.new standard_deviation: -1 }
-    expect_raises { NormaleDistribution::Persistant.new standard_deviation: 0 }
+    expect_raises(ArgumentError) { NormaleDistribution::Persistant(Int32, Float64).new standard_deviation: -1 }
+    expect_raises(ArgumentError) { NormaleDistribution::Persistant(Int32, Float64).new standard_deviation: 0 }
   end
-
 end

src/lib/binomial_distribution.cr

@@ -1,12 +1,12 @@
-class BinomialDistribution
-
-  @n : Int::All
-  @p : Number::All
+class Stats::BinomialDistribution(N, P)
+  getter n : N
+  getter p : P
 
   # @param n [Fixnum] number of tries
   # @param p [Float] probability of success
-  # @note if no probability is defined, the default value will be 0.5
-  def initialize(@n, @p = 0.5)
+  #
+  # NOTE if no probability is defined, the default value will be 0.5
+  def initialize(@n : N, @p : P = 0.5)
     raise Math::DomainError.new "The argument `p` `#{@p}` is not in greater or equal to 0" if @p < 0.0
     raise Math::DomainError.new "The argument `p` `#{@p}` is not in lesser or equal to 1" if @p > 1.0
     raise Math::DomainError.new "The argument `n` `#{@n}` is not in greater or equal to 0" if @n < 0.0
@@ -17,17 +17,15 @@ class BinomialDistribution
   end
 
   # @param k [Fixnum] number of test successful.
-  # @return [Float] probability
-  # TODO : Enumerable of Int
+  #
+  # TODO : Enumerable of Int
   def distribute(k : Enumerable)
-    k.map{|p| distribute(p) }.reduce{|a, b| a + b}
+    k.map { |p| distribute(p) }.reduce { |a, b| a + b }
   end
 
   # @param k [Enumerable] list of number of test successful.
-  # @return [Float] probability
-  def distribute(k : Int::All)
+  def distribute(k : Int)
     raise Math::SuperiorityError.new "the number of success must be lesser or equal to the number of tries (#{@n})" if k > @n
     Math.coef_binomial(@n, k) * (@p**k) * ((1 - @p) ** (@n - k))
   end
-
 end

src/lib/math.cr

@@ -0,0 +1 @@
+require "./math/*"

src/lib/math/angles.cr

@@ -0,0 +1,14 @@
+module Math::Angle
+  # Convert degree to radian
+  def radian
+    (Math::PI * self) / 180
+  end
+
+  def degree
+    (self * 180) / (Math::PI)
+  end
+end
+
+abstract struct Number
+  include Math::Angle
+end

src/lib/math/big_number.cr

@@ -1,23 +1,34 @@
-require "big_int"
-require "big_float"
+# This file defines new operations on big numbers with native data types
+
+# :nodoc:
+require "big"
 
 {% for klass in [Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64] %}
+  # :nodoc:
   struct {{klass}}
     {% for op in ["+", "-", "*", "%", "/"] %}
       {% for other_klass in [BigFloat, BigInt] %}
+        # :nodoc:
         def {{op.id}}(other : {{other_klass}})
           {{other_klass}}.new(self) {{op.id}} other
         end
       {% end %}
     {% end %}
 
+      # :nodoc:
     def unsafe_div(other : BigInt)
       BigInt.new(self) / other
     end
 
+    # :nodoc:
+    def unsafe_mod(other : BigInt)
+      BigInt.new(self) % other
+    end
+
   end
 {% end %}
 
+# :nodoc:
 struct BigInt
   {% for op in ["+", "-", "*", "%", "/"] %}
   def {{op.id}}(other : Float::Primitive)
@@ -28,4 +39,8 @@ struct BigInt
   def /(other : BigFloat)
     self / other
   end
+
+  def unsafe_shr(other : Int::All)
+    BigInt.new(self) ** other
+  end
 end

src/lib/math/coef_binomial.cr

@@ -0,0 +1,22 @@
+# :nodoc:
+require "big"
+
+require "./factorial"
+
+module Math
+  include Math::Factorial
+
+  # Computes the binomial coefficient of (n, k)
+  def coef_binomial(n : Int, k : Int)
+    return 0 if n < 0 || k < 0 || n < k
+    # puts "n=#{n},k=#{k},n-k=#{n - k}, factorial(#{n})=#{factorial(n)}, (factorial(#{n}) * factorial(#{n - k}))=#{(factorial(k) * factorial(n - k))}"
+    return factorial(n) / (factorial(k) * factorial(n - k))
+  end
+
+  # Computes the Binomial distributions of *success* among *tries* given a *probability* of success.
+  #
+  # NOTE if no named parameters are used, then it will try to use the unamed parameters (tries, success, probability).
+  def binomial_distribution(tries : Int, success : Int, probability : Number)
+    Stats::BinomialDistribution(typeof(tries), typeof(probability)).new(n: tries, p: probability).distribute(success)
+  end
+end

src/lib/math/correlation.cr

@@ -0,0 +1,25 @@
+require "./std_dev"
+
+module Math::Correlation
+  # Computes the correlation coefficient with another list
+  def correlation_coef(rhs : Enumerable)
+    raise "Impossible to computes the covariance for #{rhs.size} list (require #{size})" if rhs.size != size
+    e = self.standard_deviation * rhs.standard_deviation
+    covariance(rhs) / e
+  end
+
+  # Computes the covariance with another list
+  def covariance(rhs : Enumerable)
+    raise "Impossible to computes the covariance for #{rhs.size} list (require #{size})" if rhs.size != size
+    e = self.mean * rhs.mean
+    self.zip(rhs).map do |t|
+      x = t[0]
+      y = t[1]
+      x*y - e
+    end.mean
+  end
+end
+
+module Enumerable(T)
+  include Math::Correlation
+end

src/lib/math/exceptions.cr

@@ -1,4 +1,7 @@
 module Math
+  # :nodoc:
   class SuperiorityError < Exception; end
+
+  # :nodoc:
   class DomainError < Exception; end
 end

src/lib/math/factorial.cr

@@ -0,0 +1,10 @@
+module Math
+  module Factorial
+    # A factorial(N) = 1x2x3x...xN
+    def factorial(n : Number)
+      raise Math::DomainError.new "The argument must be a natural (out of domain -- factorial)" if n < 0
+      return (typeof(n)).new(1) if n == 0
+      return (1..n).to_a.reduce((typeof(n)).new(1)) { |a, b| a * b }
+    end
+  end
+end

src/lib/math/frequency.cr

@@ -0,0 +1,18 @@
+module Math::Frequency(T)
+  def frequency_of(value : T) : Float64
+    return 0.0f64 if empty?
+    count { |curr| curr == value }.to_f64 / size.to_f64
+  end
+
+  def all_frequencies : Hash(T, Float64)
+    values = to_set
+    frequencies = Hash(T, Float64).new(0.0f64, values.size)
+    each { |value| frequencies[value] += 1 }
+    frequencies.each { |k, _| frequencies[k] = frequencies[k] / size }
+    frequencies
+  end
+end
+
+module Enumerable(T)
+  include Math::Frequency(T)
+end

src/lib/math/macd.cr

@@ -0,0 +1,34 @@
+module Math::MACD
+  # Computes the MACD (sliding mean) over N values.
+  # It will return another list of *size - n + 1* elements, because it is not
+  # possible to computes the n/2 first and lasts means.
+  # NOTE for now it is impossible to computes a MACD with a pair window (n should be odd)
+  #
+  # TODO: maybe computing a reduced MACD is good solution against reduced returns ?
+  def macd(n : Int)
+    ((n.odd?) ? macd_odd(n) : macd_pair(n)).compact
+  end
+
+  # :nodoc:
+  #
+  # MACD computation if n is odd
+  private def macd_odd(n)
+    map_with_index do |_, i|
+      next if i < n / 2
+      next if i + n / 2 >= size
+      range = (i - n / 2)..(i + n / 2)
+      self[range].mean
+    end
+  end
+
+  # :nodoc:
+  #
+  # MACD computation if n is pair
+  private def macd_pair(n)
+    raise ArgumentError.new "The MACD should be computed for an odd window (you should retry with #{n + 1})"
+  end
+end
+
+module Enumerable(T)
+  include Math::MACD
+end

src/lib/math/mean.cr

@@ -0,0 +1,34 @@
+module Math::Mean
+  # Standard arithmetic mean
+  # TODO: Handle big Float/Int
+  def mean
+    return 0.0_f64 if empty?
+    sum.to_f64 / size.to_f64
+  end
+
+  # The root square mean of the list.
+  # TODO: Handle big Float/Int
+  def quadratic_mean
+    return 0.0_f64 if empty?
+    Math.sqrt map { |e| e ** 2 }.mean
+  end
+
+  # The geometric mean of the list.
+  # For [a, b], a/c = c/b; c**2 = a*b
+  # TODO: Handle big Float/Int
+  def geometric_mean
+    return 0.0_f64 if empty?
+    reduce { |l, r| l * r } ** (1.0 / size.to_f64)
+  end
+
+  # The harmonic mean of the list.
+  # TODO: Handle big Float/Int
+  def harmonic_mean
+    return 0.0_f64 if empty?
+    size.to_f64 / map { |e| 1.0 / e }.sum
+  end
+end
+
+module Enumerable(T)
+  include Math::Mean
+end

src/lib/math/median.cr

@@ -0,0 +1,13 @@
+module Math::Median
+  def median
+    return 0.0_f64 if empty?
+    sorted = sort
+    size = size()
+    return sorted[(size - 1) / 2] / 1.0 if size.odd?
+    (sorted[(size / 2) - 1] + sorted[size / 2]) / 2.0
+  end
+end
+
+module Enumerable(T)
+  include Math::Median
+end

src/lib/math/quartile.cr

@@ -0,0 +1,70 @@
+# There are several methods for computing the quartiles of an array.
+#
+# This library utilizes the method proposed by John Tukey
+# https://en.wikipedia.org/wiki/Quartile#Method_2
+#
+module Math::Quartile
+  def lower_quartile : Float64
+    return 0.0_f64 if empty?
+    m = self.median
+    lower_half = self.select { |i| i <= m }
+    lower_half.median
+  end
+
+  # alias
+  def first_quartile : Float64
+    lower_quartile
+  end
+
+  # alias
+  def second_quartile : Float64
+    median
+  end
+
+  def upper_quartile : Float64
+    return 0.0_f64 if empty?
+    m = self.median
+    upper_half = self.select { |i| i >= m }
+    upper_half.median
+  end
+
+  # alias
+  def third_quartile : Float64
+    upper_quartile
+  end
+
+  def quartiles : Array(Float64)
+    [first_quartile, second_quartile, third_quartile]
+  end
+
+  def iqr : Float64
+    third_quartile - first_quartile
+  end
+
+  # alias
+  def interquartile_range : Float64
+    iqr
+  end
+
+  def lower_fence(k : Number = 1.5) : Float64
+    lower_quartile - k * iqr
+  end
+
+  def upper_fence(k : Number = 1.5) : Float64
+    upper_quartile + k * iqr
+  end
+
+  def lower_outliers(k : Number = 1.5) : Array
+    lf = lower_fence k
+    self.select { |i| i < lf }
+  end
+
+  def upper_outliers(k : Number = 1.5) : Array
+    uf = upper_fence k
+    self.select { |i| i > uf }
+  end
+end
+
+module Enumerable(T)
+  include Math::Quartile
+end

src/lib/math/std_dev.cr

@@ -0,0 +1,19 @@
+require "./mean"
+
+module Math::StandardDeviation
+  # Squared deviation from the mean.
+  def variance
+    return 0.0_f64 if empty?
+    mean = mean()
+    self.map { |e| (e - mean)**2 }.mean
+  end
+
+  # Population standard deviation.
+  def standard_deviation
+    Math.sqrt variance
+  end
+end
+
+module Enumerable(T)
+  include Math::StandardDeviation
+end

src/lib/normale_distribution.cr

@@ -0,0 +1,20 @@
+require "./normale_distribution/persistant"
+
+module Stats::NormaleDistribution
+  extend self
+
+  # Gives the probability of [ min; max ] for a normal distribution (*standard_deviation*)
+  def between(standard_deviation : Number, esperance : Number, min : Number, max : Number)
+    Stats::NormaleDistribution::Persistant.new(standard_deviation: standard_deviation, esperance: esperance).between min, max
+  end
+
+  # Gives the probability of [ min; +inf [ for a normal distribution (*standard_deviation*)
+  def greater_than(standard_deviation : Number, esperance : Number, min : Number)
+    Stats::NormaleDistribution::Persistant.new(standard_deviation: standard_deviation, esperance: esperance).greater_than min
+  end
+
+  # Gives the probability of ] -inf; max ] for a normal distribution (*standard_deviation*)
+  def less_than(standard_deviation : Number, esperance : Number, max : Number)
+    Stats::NormaleDistribution::Persistant.new(standard_deviation: standard_deviation, esperance: esperance).less_than max
+  end
+end

src/lib/normale_distribution/persistant.cr

@@ -0,0 +1,33 @@
+class Stats::NormaleDistribution::Persistant(D, E)
+  property standard_deviation : D
+  property esperance : E
+
+  # Create a new normale distribution
+  def initialize(@standard_deviation : D = 1.0, @esperance : E = 0.0)
+    raise ArgumentError.new "standard_deviation must be > 0" unless @standard_deviation > 0.0
+  end
+
+  # Gives the probability of [ min; +inf [
+  def greater_than(min : Number)
+    1.0 - repartition(min)
+  end
+
+  # Gives the probability of ] -inf; max ]
+  def less_than(max : Number)
+    repartition max
+  end
+
+  # Gives the probability of [ min; max ]
+  def between(min : Number, max : Number)
+    repartition(max) - repartition(min)
+  end
+
+  # private def density(t : Number::All)
+  #   1.0 / (standard_deviation * (2 * Math::PI) ** 0.5) * Math::exp((t - esperance) / (2 * standard_deviation))
+  # end
+
+  private def repartition(t : Number)
+    erf = (t - esperance) / (standard_deviation * 2.0**0.5)
+    0.5 * (1.0 + Math.erf(erf))
+  end
+end

src/stats.cr

@@ -1,8 +1,4 @@
-#require "big_int"
-#require "big_float"
-require "./stats/*"
-require "./stats/math/*"
+# require "big"
 
-module Stats
-  # TODO Put your code here
-end
+require "./stats/*"
+require "./lib/*"

src/stats/math/coef_binomial.cr

@@ -1,21 +0,0 @@
-require "./factorial"
-require "big_int"
-
-module Math
-  {% for num_type in [Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, BigInt] %}
-    include Math::Factorial({{num_type}})
-  {% end %}
-
-  extend self
-
-  def coef_binomial(n : Int::All, k : Int::All)
-    return 0 if n < 0 || k < 0 || n < k
-    return factorial(n) / (factorial(k) * factorial(n - k))
-  end
-
-  # @note if no named parameters are used, then it will try to use the unamed parameters (tries, success, probability)
-  def binomial_distribution(tries : Int::All, success : Int::All, probability : Number::All)
-    BinomialDistribution.new(n: tries, p: probability).distribute(success)
-  end
-
-end

src/stats/math/factorial.cr

@@ -1,11 +0,0 @@
-module Math
-  module Factorial(U)
-
-    def factorial(n : U)
-      raise Math::DomainError.new "The argument must be a natural (out of domain -- factorial)" if n < 0
-      return U.new(1) if n == 0
-      return (1..n).to_a.reduce(U.new(1)){|a, b| a * b}
-    end
-
-  end
-end

src/stats/math/numeric_value.cr

@@ -1,12 +0,0 @@
-abstract struct Int
-  alias All = Int::Primitive | BigInt
-end
-
-require "big_float"
-abstract struct Float
-  alias All = Float::Primitive | BigFloat #| BigRational
-end
-
-abstract struct Number
-  alias All = Int::All | Float::All
-end

src/stats/normale_distribution.cr

@@ -1,19 +0,0 @@
-require "./normale_distribution/persistant"
-
-module NormaleDistribution
-
-  def between(standard_deviation : Number::All, esperance : Number::All, min : Number::All, max : Number::All)
-    NormaleDistribution::Persistant.new(standard_deviation: standard_deviation, esperance: esperance).between min, max
-  end
-
-  def greater_than(standard_deviation : Number::All, esperance : Number::All, min : Number::All)
-    NormaleDistribution::Persistant.new(standard_deviation: standard_deviation, esperance: esperance).greater_than min
-  end
-
-  def less_than(standard_deviation : Number::All, esperance : Number::All, max : Number::All)
-    NormaleDistribution::Persistant.new(standard_deviation: standard_deviation, esperance: esperance).less_than max
-  end
-
-  extend self
-
-end

src/stats/normale_distribution/persistant.cr

@@ -1,36 +0,0 @@
-module NormaleDistribution
-  class Persistant
-
-    getter standard_deviation, esperance
-    setter standard_deviation, esperance
-
-    @standard_deviation : Number::All
-    @esperance          : Number::All
-
-    def initialize(@standard_deviation = 1.0, @esperance = 0.0)
-      raise ArgumentError.new "standard_deviation must be > 0" unless @standard_deviation > 0.0
-    end
-
-    def greater_than(min : Number::All)
-      1.0 - repartition(min)
-    end
-
-    def less_than(max : Number::All)
-      repartition max
-    end
-
-    def between(min : Number::All, max : Number::All)
-      repartition(max) - repartition(min)
-    end
-
-    private def density(t : Number::All)
-      #1.0 / (standard_deviation * (2 * Math::PI) ** 0.5) * Math::exp((t - esperance) / (2 * standard_deviation)))
-    end
-
-    private def repartition(t : Number::All)
-      erf = (t - esperance) / (standard_deviation * 2.0**0.5)
-      0.5 * (1.0 + Math.erf(erf))
-    end
-
-  end
-end

src/stats/version.cr

@@ -1,3 +1,3 @@
 module Stats
-  VERSION = "0.1.0"
+  VERSION = "0.3"
 end