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module Statistics
module Distribution
class LogSeries
def self.density_function(k, p)
return if k <= 0
k = k.to_i
left = (-1.0 / Math.log(1.0 - p))
right = (p ** k).to_f
left * right / k
end
def self.cumulative_function(k, p)
return if k <= 0
# Sadly, the incomplete beta function is converging
# too fast to zero and breaking the calculation on logs.
# So, we default to the basic definition of the CDF which is
# the integral (-Inf, K) of the PDF, with P(X <= x) which can
# be solved as a summation of all PDFs from 1 to K. Note that the summation approach
# only applies to discrete distributions.
#
# right = Math.incomplete_beta_function(p, (k + 1).floor, 0) / Math.log(1.0 - p)
# 1.0 + right
result = 0.0
1.upto(k) do |number|
result += self.density_function(number, p)
end
result
end
def self.mode
1.0
end
def self.mean(p)
(-1.0 / Math.log(1.0 - p)) * (p / (1.0 - p))
end
def self.variance(p)
up = p + Math.log(1.0 - p)
down = ((1.0 - p) ** 2) * (Math.log(1.0 - p) ** 2)
(-1.0 * p) * (up / down.to_f)
end
end
end
end
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