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module Distribution
module Uniform
module Ruby_
# Module contain pure ruby implementation of the
# uniform distribution (rng, pdf, cdf and quantile functions)
class << self
# Returns a lambda that emits a uniformly distributed
# sequence of random numbers between the defined limits
#
# == Arguments
# * +lower+ - Lower limit of the distribution
# * +upper+ - Upper limit of the distribution
# * +seed+ - Seed to set the initial state, randomized if ommited
#
def rng(lower = 0, upper = 1, seed = nil)
seed = Random.new_seed if seed.nil?
prng = Random.new(seed)
-> { prng.rand * (upper - lower) + lower }
end
# Uniform probability density function on [a, b]
#
# == Arguments
# If you are referring the wiki page for this continuous distribution
# the arguments can be translated as follows
# * +x+ - same as continuous random variable
# * +lower+ - lower limit or a, must be a real number
# * +upper+ - upper limit or b, must be a real number
#
# == Reference
# * https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
#
# The implementation has been adopted from GSL-1.9 gsl/randist/flat.c
#
def pdf(x, lower = 0, upper = 1)
upper, lower = lower, upper if lower > upper
return 1 / (upper - lower) if (lower..upper).member? x
0
end
# The uniform cumulative density function (CDF)
# == Arguments
# If you are referring the wiki page for this continuous distribution
# the arguments can be translated as follows
# * +x+ - same as continuous random variable
# * +lower+ - lower limit or a, must be a real number
# * +upper+ - upper limit or b, must be a real number
#
# == Reference
# * https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
#
# The implementation has been adpoted from GSL-1.9 gsl/cdf/flat.c
#
def cdf(x, lower = 0, upper = 1)
if x < lower
0
elsif x > upper
1
else
(x - lower) / (upper - lower)
end
end
# The uniform inverse CDF density function / P-value function
# == Arguments
# If you are referring the wiki page for this continuous distribution
# the arguments can be translated as follows
# * +qn+ - same as integral value
# * +lower+ - lower limit or a, must be a real number
# * +upper+ - upper limit or b, must be a real number
#
# == Returns
# * nil if the integral value is not in [0, 1]
# * inverse cdf otherwise
# == Reference
# * https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
#
# The implementation has been adpoted from GSL-1.9 gsl/cdf/flatinv.c
#
def quantile(qn, lower = 0, upper = 1)
fail RangeError, 'cdf value(qn) must be from [0, 1]. '\
"Cannot find quantile for qn=#{qn}" if qn > 1 || qn < 0
qn * upper + (1 - qn) * lower
end
alias p_value quantile
end
end
end
end
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