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module Statistics
module Distribution
class Poisson
attr_accessor :expected_number_of_occurrences
alias_method :mean, :expected_number_of_occurrences
alias_method :variance, :expected_number_of_occurrences
def initialize(l)
self.expected_number_of_occurrences = l
end
def probability_mass_function(k)
return if k < 0 || expected_number_of_occurrences < 0
k = k.to_i
upper = (expected_number_of_occurrences ** k) * Math.exp(-expected_number_of_occurrences)
lower = Math.factorial(k)
upper/lower.to_f
end
def cumulative_function(k)
return if k < 0 || expected_number_of_occurrences < 0
k = k.to_i
upper = Math.lower_incomplete_gamma_function((k + 1).floor, expected_number_of_occurrences)
lower = Math.factorial(k.floor)
# We need the right tail, i.e.: The upper incomplete gamma function. This can be
# achieved by doing a substraction between 1 and the lower incomplete gamma function.
1 - (upper/lower.to_f)
end
end
end
end
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