Class: Statistical::Distribution::TwoPoint

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

Overview

Note:

The states used to represent success & failure must be Numeric. Using it on generic state lables can cause strange outcomes!

Note:

state_failure < state_sucesss, for the sake of sanity.

Two-Point distribution implementation that uses generic labels for states that it’s random variables can take. The assumptions made would be that the states are comparable and failure < success in whatever scheme of comparison that the state objects implement. This defaults to behaving as the bernoulli distribution

Author:

  • Vaibhav Yenamandra

Direct Known Subclasses

Bernoulli

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(prob_success = 0.5, state_failure = 0, state_success = 1) ⇒ TwoPoint

Note:

The states used to represent success & failure must be Numeric. Using it on generic state lables can cause strange outcomes!

Note:

state_failure < state_sucesss, required to have a sane CDF.

Returns a new instance of the TwoPoint distribution

Parameters:

  • prob_success (Float) (defaults to: 0.5) —

    The probability of success

  • state_success (Numeric) (defaults to: 1) —

    An object to describe the 1-state of success

  • state_failure (Numeric) (defaults to: 0) —

    An object to describe the 0-state of failure



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# File 'lib/statistical/distribution/two_point.rb', line 37

def initialize(prob_success = 0.5, state_failure = 0, state_success = 1)
  if state_failure == state_success
    raise ArgumentError,
          'Success & failure must be two distinct states'
  end

  if state_failure > state_success
    raise ArgumentError,
          'Failure state must be smaller that the success state!'
  end

  unless (state_failure + state_success).is_a?(Numeric)
    raise ArgumentError,
          "States must be Numeric! Found #{state_failure.class} and #{state_success.class}"
  end

  if prob_success > 1 || prob_success < 0
    raise ArgumentError,
          "Probabilty of success must be within [0, 1]. Found #{prob_success}"
  end

  @p = prob_success
  @q = 1 - prob_success
  @states = {
    failure: state_failure,
    success: state_success
  }
  @support = @states.values.sort
  self
end

Instance Attribute Details

#p ⇒ Object (readonly)

This is probably the best but the least descriptive variable name



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# File 'lib/statistical/distribution/two_point.rb', line 21

def p
  @p
end

#q ⇒ Object (readonly)

This is probably the best but the least descriptive variable name



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# File 'lib/statistical/distribution/two_point.rb', line 21

def q
  @q
end

#states ⇒ Object (readonly)

This is probably the best but the least descriptive variable name



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# File 'lib/statistical/distribution/two_point.rb', line 21

def states
  @states
end

#support ⇒ Object (readonly)

This is probably the best but the least descriptive variable name



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# File 'lib/statistical/distribution/two_point.rb', line 23

def support
  @support
end

Instance Method Details

#cdf(x) ⇒ Float

Returns value of cumulative density function at a point. Calculated

using some technique that you might want to name

Parameters:

  • x (Numeric) —

    The state the the random variable takes. Can be 0, 1

Returns:

  • (Float) —

    The cumulative probability over all of the random variates states.



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# File 'lib/statistical/distribution/two_point.rb', line 87

def cdf(x)
  return 0 if x < @states[:failure]
  return @q if x.between?(@states[:failure], @states[:success])
  return 1 if x >= @states[:success]
end

#mean ⇒ Object

Returns the expected mean value for the calling instance.

Returns:

  • Mean of the distribution



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# File 'lib/statistical/distribution/two_point.rb', line 109

def mean
  return @p * @states[:success] + @q * @states[:failure]
end

#pdf(x) ⇒ Float

Returns value of probability density function at a given state of the random variate X. Essentially: “what’s P(X=x)?”

Parameters:

  • x (Numeric) —

    The state the the random variable takes. Can be 0, 1

Returns:

  • (Float) —

    • p if state (x) is 1.

Raises:

  • (ArgumentError) —

    if x is not of the states this instance was initialized with



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# File 'lib/statistical/distribution/two_point.rb', line 75

def pdf(x)
  return @p if @states[:success] == x
  return @q if @states[:failure] == x
  return 0
end

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

Returns value of inverse CDF for a given probability

Parameters:

  • p (Numeric) —

    a value within [0, 1]

Returns:

  • Inverse CDF for valid p

Raises:

  • (RangeError) —

    if p > 1 or p < 0

See Also:



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# File 'lib/statistical/distribution/two_point.rb', line 100

def quantile(p)
  raise RangeError, "`p` must be in [0, 1], found: #{p}" if p < 0 || p > 1
  return @states[:failure] if p <= @q
  return @states[:success] if p > @q
end

#variance ⇒ Object

Returns the expected value of variance for the calling instance.

Returns:

  • Variance of the distribution



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# File 'lib/statistical/distribution/two_point.rb', line 116

def variance
  return @p * (@states[:success]**2) + @q * (@states[:failure]**2) -
         (mean**2)
end