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module Distribution
module Poisson
module Ruby_
class << self
# Return a Proc object which returns a random number drawn
# from the poisson distribution with lambda.
#
# == Arguments
# * +lambda_val+ - mean of the poisson distribution
# * +seed+ - seed, an integer value to set the initial state
#
# == Algorithm
# * Donald Knuth
#
def rng(lambda_val = 1, seed = nil)
seed = Random.new_seed if seed.nil?
r = Random.new(seed).rand
x = 0
l = Math.exp(-lambda_val)
s = l
while r > s
x += 1
l *= lambda_val / x.to_f
s += l
end
x
end
def pdf(k, l)
(l**k * Math.exp(-l)).quo(Math.factorial(k))
end
def cdf(k, l)
Math.exp(-l) * (0..k).inject(0) { |ac, i| ac + (l**i).quo(Math.factorial(i)) }
end
def quantile(prob, l)
ac = 0
(0..100).each do |i|
ac += pdf(i, l)
return i if prob <= ac
end
end
alias_method :p_value, :quantile
end
end
end
end
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