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# Added by John O. Woods, SciRuby project.
# Optimized by Claudio Bustos
module Distribution
module Hypergeometric
module Ruby_
class << self
def bc(n, k)
Math.binomial_coefficient(n, k)
end
# Hypergeometric probability density function
#
# Probability p(+k+, +m+, +n+, +total+) of drawing sets of size +m+ and +n+ with an intersection of size +k+
# from a total pool of size +total+, without replacement.
#
# ==References
# * http://www.gnu.org/software/gsl/manual/html_node/The-Hypergeometric-Distribution.html
# * http://en.wikipedia.org/wiki/Hypergeometric_distribution
def pdf(k, m, n, total)
min_m_n = m < n ? m : n
max_t = [0, m + n - total].max
return 0 if k > min_m_n || k < max_t
(bc(m, k) * bc(total - m, n - k)).quo(bc(total, n))
end
alias_method :exact_pdf, :pdf
def pdf_with_den(k, m, n, total, den)
(bc(m, k) * bc(total - m, n - k)).quo(den)
end
# Cumulative distribution function.
# The probability of obtain, from a sample of
# size +n+, +k+ or less elements
# in a population size +total+ with +m+ interesting elements.
#
# Slow, but secure
def cdf(k, m, n, total)
fail(ArgumentError, 'k>m') if k > m
fail(ArgumentError, 'k>n') if k > n
# Store the den
den = bc(total, n)
(0..k).collect { |ki| pdf_with_den(ki, m, n, total, den) }.inject { |sum, v| sum + v }
end
alias_method :exact_cdf, :cdf
# p-value:
def quantile(pr, m, n, total)
ac = 0
den = bc(total, n)
(0..total).each do |i|
ac += pdf_with_den(i, m, n, total, den)
return i if ac >= pr
end
end
alias_method :p_value, :quantile
alias_method :exact_p_value, :p_value
end
end
end
end
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