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#include <cmath>#include <iostream>
Go to the source code of this file.
The Poisson distribution counts how many events occur over a set time interval.
Definition in file poisson_dist.cpp.
◆ fact()Compute factorial of a given number
Definition at line 30 of file poisson_dist.cpp.
30 {
31 double x_fact = x;
32 for (int i = x - 1; i > 0; i--) {
33 x_fact *= i;
34 }
35
36 if (x_fact <= 0) {
37 x_fact = 1;
38 }
39 return x_fact;
40}
◆ main()main function
Definition at line 65 of file poisson_dist.cpp.
65 {
66 double rate, expected;
68 std::cout << "Poisson rate : " << rate << std::endl;
69
71 std::cout << "Poisson expected : " << expected << std::endl;
72
74 << std::endl;
75 std::cout << "Poisson 0-8 successes : "
77
78 return 0;
79}
double poisson_x_successes(double expected, double x)
double poisson_rate(double events, double timeframe)
double poisson_expected(double rate, double time)
double poisson_range_successes(double expected, double lower, double upper)
◆ poisson_expected() double poisson_expected ( double rate, double time )calculate the expected value over a time e.g rate of 2.5 over 10 mins = 2.5 x 10 = 25
Definition at line 25 of file poisson_dist.cpp.
25{ return rate * time; }
◆ poisson_range_successes() double poisson_range_successes ( double expected, double lower, double upper )probability of a success in range for Poisson dist (inclusive, inclusive)
\[P = \sum_i p(\mu,i)\]
Definition at line 54 of file poisson_dist.cpp.
54 {
56 for(
inti =
lower; i <= upper; i++) {
58 }
60}
std::string lower(std::string word)
function to convert a C++ string to lower case
◆ poisson_rate() double poisson_rate ( double events, double timeframe )poisson rate:
calculate the events per unit time
e.g 5 dollars every 2 mins = 5 / 2 = 2.5
Definition at line 17 of file poisson_dist.cpp.
17 {
18 return events / timeframe;
19}
◆ poisson_x_successes() double poisson_x_successes ( double expected, double x )Find the probability of x successes in a Poisson dist.
\[p(\mu,x) = \frac{\mu^x e^{-\mu}}{x!}\]
Definition at line 46 of file poisson_dist.cpp.
46 {
47 return(std::pow(expected, x) * std::exp(-expected)) /
fact(x);
48}
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