Class: Statistical::Distribution::UniformDiscrete

Inherits:
Object
  • Object
show all
Defined in:
lib/statistical/distribution/uniform_discrete.rb

Overview

This class abstracts the discrete uniform distribution over a given set

of elements

random variate from the distribution can take. Must have at least 1 value

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(elems) ⇒ UniformDiscrete

Note:

The constructor sorts the array of elements given to it, as this is a key assumption of the discrete uniform distribution. This set must also be homogenous

Returns a model for the discrete uniform distribution on all elements present in the given set of elemets elems

Parameters:

  • elems (Array) —

    The elements over which the distribution exists in [lower, upper]

Raises:

  • (RangeError) —

    if elems isn’t one of Array, Range, Fixnum or Bignum



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 27

def initialize(elems)
  case elems
  when Fixnum, Bignum
    @support = [elems]
  when Array
    @support = elems.sort
  when Range
    @support = elems.to_a
  else
    raise ArgumentError,
          "Expected Fixnum, Bignum, Array or Range, found #{elems.class}"
  end
  @count = @support.length
  @lower = @support[0]
  @upper = @support[-1]
  self
end

Instance Attribute Details

#count ⇒ Object (readonly)

Returns the value of attribute count.



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 15

def count
  @count
end

#lower ⇒ Object (readonly)

Returns the value of attribute lower.



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 15

def lower
  @lower
end

#support ⇒ Array, Numeric (readonly)

The support set of valid values a

Returns:

  • (Array, Numeric) —

    the current value of support



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 12

def support
  @support
end

#upper ⇒ Object (readonly)

Returns the value of attribute upper.



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 15

def upper
  @upper
end

Instance Method Details

#cdf(k) ⇒ Float

Note:

This suffers from some floating point comparison issues. Errors start appearing when dealing with precision > 1E-18

Returns value of cumulative density function at a point on the real line Uses a binary search on the support array internally.

Parameters:

  • k (Fixnum, Bignum) —

    Point at which cdf value is desired

Returns:

  • (Float) —

    0 if k is on the left of the support, 1 if k on the right support and the evaluates CDF for any other legal value



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 67

def cdf(k)
  return 0.0 if k < @lower
  return 1.0 if k >= @upper

  # Ruby has a Array#bsearch_index already but it supports find-min mode
  # What we need is a find-max mode. This can be achieved by reversing
  # and then searching, but reverse is O(N) so it defeats the purpose
  low = 0
  high = @count - 1
  while low < high
    mid = (low + high) / 2
    if @support[mid] <= k
      low = mid + 1
    else
      high = mid
    end
  end
  # This should be true for all i > low
  return low.fdiv(@count)
end

#mean ⇒ Float

Returns the mean value for the calling instance. Calculated mean, and

not inferred from simulations

Returns:

  • (Float) —

    Mean of the distribution



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 106

def mean
  return @support.mean
end

#pdf(k) ⇒ Float

Returns value of probability density function at a point on the real

line

Parameters:

  • k (Fixnum, Bignum) —

    Point at which pdf is desired

Returns:

  • (Float) —

    0 if k doesn’t belong to the elements over which the current instance is distributed. 1/n otherwise where n is number of elements



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 52

def pdf(k)
  return 1.0 / @count if @support.include?(k)
  return 0.0
end

#quantile(p) ⇒ Numeric Also known as: p_value

Returns value of inverse CDF for a given probability.

Parameters:

  • p (Numeric) —

    a value within [0, 1]

Returns:

  • (Numeric) —

    Returns inverse CDF for valid p

Raises:

  • (RangeError) —

    if p > 1 or p < 0

See Also:



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 95

def quantile(p)
  raise RangeError, "`p` must be in [0, 1], found: #{p}" if p < 0 || p > 1
  return @lower if p.zero?
  return @upper if (p - 1).zero?
  return @support[(p * count).ceil - 1]
end

#variance ⇒ Float

Returns the expected value of population variance for the calling

instance.

Returns:

  • (Float) —

    Variance of the distribution



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# File 'lib/statistical/distribution/uniform_discrete.rb', line 114

def variance
  return @support.pvariance
end