Module: Distribution::F::Ruby_

Extended by:
MathExtension
Defined in:
lib/distribution/f/ruby.rb

Overview

The upper and lower cumulative distribution functions are related by P(x) + Q(x) = 1 and satisfy 0 <= P(x) <= 1, 0 <= Q(x).

Constant Summary

Constants included from MathExtension

MathExtension::EULER, MathExtension::LN2, MathExtension::LNPI, MathExtension::LOG_FLOAT_MIN, MathExtension::ROOT3_FLOAT_EPSILON, MathExtension::ROOT3_FLOAT_MIN, MathExtension::ROOT4_FLOAT_EPSILON, MathExtension::ROOT4_FLOAT_MIN, MathExtension::ROOT5_FLOAT_EPSILON, MathExtension::ROOT5_FLOAT_MIN, MathExtension::ROOT6_FLOAT_EPSILON, MathExtension::ROOT6_FLOAT_MIN, MathExtension::SQRT2, MathExtension::SQRTPI

Class Method Summary collapse

Methods included from MathExtension

beta, binomial_coefficient, binomial_coefficient_gamma, binomial_coefficient_multiplicative, erfc_e, exact_regularized_beta, exp_err, factorial, fast_factorial, gammq, incomplete_beta, incomplete_gamma, lbeta, logbeta, loggamma, permutations, regularized_beta, rising_factorial, unnormalized_incomplete_gamma

Class Method Details

.cdf(x, n, m) ⇒ Object

Cumulative Distribution Function.



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# File 'lib/distribution/f/ruby.rb', line 44

def cdf(x, n, m)
  x = x.to_f
  xx = (x * n).to_f / (x * n + m).to_f
  regularized_beta(xx, n / 2.0, m / 2.0)
end

.entropy ⇒ Object 



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# File 'lib/distribution/f/ruby.rb', line 111

def entropy
end

.kurtosis ⇒ Object 



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# File 'lib/distribution/f/ruby.rb', line 108

def kurtosis
end

.mean ⇒ Float

Return the corresponding F value for a p-value y with n and m degrees of freedom.

Parameters:

  • y (Float) —

    Value corresponding to the desired p-value. Between 0 and 1.

  • n (Float) —

    Degree of freedom of the first random variable.

  • m (Float) —

    Degree of freedom of the second random variable.

Returns:

  • (Float) —

    Value of the F distribution that gives a p-value of y.



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# File 'lib/distribution/f/ruby.rb', line 99

def mean
end

.mode ⇒ Object 



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# File 'lib/distribution/f/ruby.rb', line 102

def mode
end

.pdf(x, n, m) ⇒ Object

F Distribution (Ruby) -- Probability Density Function



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# File 'lib/distribution/f/ruby.rb', line 35

def pdf(x, n, m)
  x = x.to_f
  numerator = ((n * x)**n * (m**m)) / (n * x + m)**(n + m)
  denominator = x * Math.beta(n / 2.0, m / 2.0)

  Math.sqrt(numerator) / denominator
end

.q(x, n, m) ⇒ Object

Upper cumulative function.

If cdf(x, n, m) = p, then q(x, n, m) = 1 - p



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# File 'lib/distribution/f/ruby.rb', line 53

def q(x, n, m)
  1.0 - cdf(x, n, m)
end

.quantile(probability, n, m) ⇒ Object Also known as: p_value

Return the F value corresponding to probability with degrees of freedom n and m.

If x = quantile(p, n, m), then cdf(x, n, m) = p.

Taken from: https://github.com/JuliaLang/Rmath-julia/blob/master/src/qf.c



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# File 'lib/distribution/f/ruby.rb', line 64

def quantile(probability, n, m)
  return Float::NAN if n <= 0.0 || m <= 0.0

  if n == Float::INFINITY || n == -Float::INFINITY || m == Float::INFINITY || m == -Float::INFINITY
    return 1.0
  end

  if n <= m && m > 4e5
    return Distribution::ChiSquare.p_value(probability, n) / n.to_f
  elsif n > 4e5 # thus n > m
    return m.to_f / Distribution::ChiSquare.p_value(1.0 - probability, m)
  else
    # O problema está aqui.
    tmp = Distribution::Beta.p_value(1.0 - probability, m.to_f / 2, n.to_f / 2)
    value = (1.0 / tmp - 1.0) * (m.to_f / n.to_f)
    return value.nan? ? Float::NAN : value
  end
end

.skewness ⇒ Object 



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# File 'lib/distribution/f/ruby.rb', line 105

def skewness
end