Class: Digiproc::Probability::TheoreticalBinomialDistribution

Inherits:
Object
  • Object
show all
Defined in:
lib/probability/binomial_distribution.rb

Overview

Allows you to solve problems whose probabilities are dictated by a binomial distribution Does not simulate a problem, but calculates probabilities based off of the binomial distribution equation See examples/binomial_distribution/dice.rb

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(n:, k: nil, p:) ⇒ TheoreticalBinomialDistribution

Initialize with n, k, and p

n
Integer

Number of trials

k
Integer

(optional at initialization) Number of successes

p
Numeric

Probability of success



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# File 'lib/probability/binomial_distribution.rb', line 15

def initialize(n: ,k: nil , p: )
    @n = n
    @k = k
    @p = p
end

Instance Attribute Details

#k ⇒ Object

Returns the value of attribute k.



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# File 'lib/probability/binomial_distribution.rb', line 8

def k
  @k
end

#n ⇒ Object

Returns the value of attribute n.



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# File 'lib/probability/binomial_distribution.rb', line 8

def n
  @n
end

#p ⇒ Object

Returns the value of attribute p.



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# File 'lib/probability/binomial_distribution.rb', line 8

def p
  @p
end

Instance Method Details

#coeff ⇒ Object

Will run ‘coefficient` method using `self.k` bd.coeff # => 252.0



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# File 'lib/probability/binomial_distribution.rb', line 49

def coeff
    coefficient(self.k)
end

#coefficient(k = self.k) ⇒ Object

Returns the binomial equation coefficient for a given number of wins, ie returns n! / (k! * (n - k)!) Can take an argument of ‘k`, which defaults to `self.k` Returns a BigDecimal bd.coefficient(4) # => 210.0



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# File 'lib/probability/binomial_distribution.rb', line 77

def coefficient(k = self.k)
    n_fact = BigDecimal(Digiproc::Functions.fact(self.n))
    k_fact = BigDecimal(Digiproc::Functions.fact(k))
    n_fact / (k_fact * BigDecimal((Digiproc::Functions.fact(self.n - k))))
end

#expect ⇒ Object

Returns the Expected Value of a binomial distributed random variable (n * p) bd = Digiproc::Probability::TheoreticalBinomialDistribution.new(n:10, p: 0.5) bd.expect # => 5 ie in above example, expect 5 successes (heads) in 10 flips of a coin



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# File 'lib/probability/binomial_distribution.rb', line 26

def expect
    self.n * self.p
end

#prob ⇒ Object

Will run ‘probability` method using `self.k` bd.k = 5 bd.prob # => 0.24609375



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# File 'lib/probability/binomial_distribution.rb', line 42

def prob
    self.probability(self.k)
end

#probability(*k) ⇒ Object

Calculates the probability of ‘k` number of `wins` `k` can be an array or a range of numbers, a variable number of args, or a single integer (see example referenced above) If k is more than one value, the probabilities will be summed together For example: bd.probability(5) # => 0.24609375 bd.probability(0..5) # => 0.623046875 bd.probability(1,2,5,6) # => 0.5048828125 bd.probability() # => 0.623046875



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# File 'lib/probability/binomial_distribution.rb', line 62

def probability(*k)
    sum = 0
    karr = k.map{ |val| val.respond_to?(:to_a) ? val.to_a : val}
    karr.flatten!
    karr.each do |k_val| 
        sum += self.coefficient(k_val) * ((self.p) ** (k_val)) * (1 - self.p) ** (n - k_val)
    end
    sum.to_f
end

#var ⇒ Object

Return the Variance of the binomial distributed random variable (n * p * (1 - p)) Using above example: bd.var # => 2.5



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# File 'lib/probability/binomial_distribution.rb', line 34

def var
    self.n * self.p * ( 1 - self.p )
end