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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 or k<max_t
(bc(m,k) * bc(total-m,n-k)).quo(bc(total,n))
end
def pdf_with_den(k,m,n,total,den)
(bc(m,k) * bc(total-m,n-k)).quo(den)
end
# p-value:
def p_value(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
# 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)
raise(ArgumentError, "k>m") if k>m
raise(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 :exact_pdf :pdf
alias :exact_p_value :p_value
alias :exact_cdf :cdf
end
end
end
end
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