Algorithms_in_C++  1.0.0
Set of algorithms implemented in C++.
binomial_dist.cpp File Reference

Binomial distribution example More...

#include <cmath>
#include <iostream>
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Functions

double binomial_expected (double n, double p)
 
double binomial_variance (double n, double p)
 
double binomial_standard_deviation (double n, double p)
 
double nCr (double n, double r)
 
double binomial_x_successes (double n, double p, double x)
 
double binomial_range_successes (double n, double p, double lower_bound, double upper_bound)
 
int main ()
 

Detailed Description

Binomial distribution example

The binomial distribution models the number of successes in a sequence of n independent events

Summary of variables used:

  • n : number of trials
  • p : probability of success
  • x : desired successes

Function Documentation

◆ binomial_expected()

double binomial_expected ( double  n,
double  p 
)

finds the expected value of a binomial distribution

Parameters
[in]n
[in]p
Returns
\(\mu=np\)
22 { return n * p; }

◆ binomial_range_successes()

double binomial_range_successes ( double  n,
double  p,
double  lower_bound,
double  upper_bound 
)

calculates the probability of a result within a range (inclusive, inclusive)

Returns
\(\displaystyle \left.P(n,p)\right|_{x_0}^{x_1} = \sum_{i=x_0}^{x_1} P(i) =\sum_{i=x_0}^{x_1} {n\choose i} p^i (1-p)^{n-i}\)
75  {
76  double probability = 0;
77  for (int i = lower_bound; i <= upper_bound; i++) {
78  probability += nCr(n, i) * std::pow(p, i) * std::pow(1 - p, n - i);
79  }
80  return probability;
81 }
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◆ binomial_standard_deviation()

double binomial_standard_deviation ( double  n,
double  p 
)

finds the standard deviation of the binomial distribution

Parameters
[in]n
[in]p
Returns
\(\sigma = \sqrt{\sigma^2} = \sqrt{n\cdot p\cdot (1-p)}\)
36  {
37  return std::sqrt(binomial_variance(n, p));
38 }
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◆ binomial_variance()

double binomial_variance ( double  n,
double  p 
)

finds the variance of the binomial distribution

Parameters
[in]n
[in]p
Returns
\(\sigma^2 = n\cdot p\cdot (1-p)\)
29 { return n * p * (1 - p); }

◆ binomial_x_successes()

double binomial_x_successes ( double  n,
double  p,
double  x 
)

calculates the probability of exactly x successes

Returns
\(\displaystyle P(n,p,x) = {n\choose x} p^x (1-p)^{n-x}\)
65  {
66  return nCr(n, x) * std::pow(p, x) * std::pow(1 - p, n - x);
67 }
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◆ main()

int main ( void  )

main function

84  {
85  std::cout << "expected value : " << binomial_expected(100, 0.5)
86  << std::endl;
87 
88  std::cout << "variance : " << binomial_variance(100, 0.5) << std::endl;
89 
90  std::cout << "standard deviation : "
91  << binomial_standard_deviation(100, 0.5) << std::endl;
92 
93  std::cout << "exactly 30 successes : " << binomial_x_successes(100, 0.5, 30)
94  << std::endl;
95 
96  std::cout << "45 or more successes : "
97  << binomial_range_successes(100, 0.5, 45, 100) << std::endl;
98 
99  return 0;
100 }
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◆ nCr()

double nCr ( double  n,
double  r 
)

Computes n choose r

Parameters
[in]n
[in]r
Returns
\(\displaystyle {n\choose r} = \frac{n!}{r!(n-r)!} = \frac{n\times(n-1)\times(n-2)\times\cdots(n-r)}{r!} \)
47  {
48  double numerator = n;
49  double denominator = r;
50 
51  for (int i = n - 1; i >= ((n - r) + 1); i--) {
52  numerator *= i;
53  }
54 
55  for (int i = 1; i < r; i++) {
56  denominator *= i;
57  }
58 
59  return numerator / denominator;
60 }
std::sqrt
T sqrt(T... args)
std::cout
binomial_range_successes
double binomial_range_successes(double n, double p, double lower_bound, double upper_bound)
Definition: binomial_dist.cpp:74
binomial_standard_deviation
double binomial_standard_deviation(double n, double p)
Definition: binomial_dist.cpp:36
binomial_x_successes
double binomial_x_successes(double n, double p, double x)
Definition: binomial_dist.cpp:65
std::upper_bound
T upper_bound(T... args)
binomial_expected
double binomial_expected(double n, double p)
Definition: binomial_dist.cpp:22
std::endl
T endl(T... args)
nCr
double nCr(double n, double r)
Definition: binomial_dist.cpp:47
binomial_variance
double binomial_variance(double n, double p)
Definition: binomial_dist.cpp:29
std::pow
T pow(T... args)