Module: Distribution::Beta::Ruby_

Extended by:
Math
Defined in:
lib/distribution/beta/ruby.rb

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 Math

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

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, a, b) ⇒ Object

Gamma cumulative distribution function Translated from GSL-1.9: cdf/beta.c gsl_cdf_beta_P


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# File 'lib/distribution/beta/ruby.rb', line 31

def cdf(x, a, b)
  return 0.0 if x <= 0.0
  return 1.0 if x >= 1.0
  Math::IncompleteBeta.axpy(1.0, 0.0, a, b, x)
end

.pdf(x, a, b) ⇒ Object

Beta distribution probability density function

Adapted from GSL-1.9 (apparently by Knuth originally), found in randist/beta.c

Form: p(x) dx = (Gamma(a + b)/(Gamma(a) Gamma(b))) x^(a-1) (1-x)^(b-1) dx

== References


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# File 'lib/distribution/beta/ruby.rb', line 15

def pdf(x, a, b)
  return 0 if x < 0 || x > 1

  gab = Math.lgamma(a + b).first
  ga  = Math.lgamma(a).first
  gb  = Math.lgamma(b).first

  if x == 0.0 || x == 1.0
    Math.exp(gab - ga - gb) * x**(a - 1) * (1 - x)**(b - 1)
  else
    Math.exp(gab - ga - gb + Math.log(x) * (a - 1) + Math::Log.log1p(-x) * (b - 1))
  end
end

.quantile(p, a, b, rmin = 0, rmax = 1) ⇒ Object Also known as: p_value

Inverse of the beta distribution function


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# File 'lib/distribution/beta/ruby.rb', line 38

def quantile(p, a, b, rmin = 0, rmax = 1)
  fail 'a <= 0' if a <= 0
  fail 'b <= 0' if b <= 0
  fail 'rmin == rmax' if rmin == rmax
  fail 'p <= 0' if p <= 0
  fail 'p > 1' if p > 1

  precision = 8.88e-016
  max_iterations = 256

  ga = 0
  gb = 2

  i = 1
  while ((gb - ga) > precision) && (i < max_iterations)
    guess = (ga + gb) / 2.0
    result = cdf(guess, a, b)

    if (result == p) || (result == 0)
      gb = ga
    elsif result > p
      gb = guess
    else
      ga = guess
    end

    fail 'No value' if i == max_iterations

    i += 1
  end

  rmin + guess * (rmax - rmin)
end