require "stats"
include Stats

NormaleDistribution.between # less_than, greater_than
  standard_deviation: 15,
  esperance: 100,
  min: 85,
  max: 115
  # => 0.6826894921370859

Math.binomial_distribution(
  tries: 3,
  probability: 0.5,
  success: 1)
  # => 0.375

Math.coef_binomial(5, 2) # => 10

Math.factorial(4) # => 24

90.radian # => (Math::PI / 2)
(Math::PI / 4) # => 45.0

[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]

[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

[1, 2, 5].median # => 2.0
[42, 1337].median # => 685.5

[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])

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]

[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}