exponential_dist.cpp File Reference

Exponential Distribution More...

#include <cassert>
#include <cmath>
#include <iostream>
#include <stdexcept>
#include <string>

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Namespaces
namespace	probability
	Probability algorithms.
namespace	exponential_dist
	Functions for the Exponential Distribution algorithm implementation.

Functions
double	probability::geometric_dist::exponential_expected (double lambda)
	the expected value of the exponential distribution
double	probability::geometric_dist::exponential_var (double lambda)
	the variance of the exponential distribution
double	probability::geometric_dist::exponential_std (double lambda)
	the standard deviation of the exponential distribution
static void	test ()
	Self-test implementations.
int	main ()
	Main function.

Detailed Description

Exponential Distribution

The exponential distribution is used to model events occuring between a Poisson process like radioactive decay.

\[P(x, \lambda) = \lambda e^{-\lambda x}\]

Summary of variables used: \(\lambda\) : rate parameter

Definition in file exponential_dist.cpp.

Function Documentation

exponential_expected()

double probability::geometric_dist::exponential_expected

(

double

lambda

)

the expected value of the exponential distribution

Returns

\[\mu = \frac{1}{\lambda}\]

Definition at line 37 of file exponential_dist.cpp.

                                           {
    if (lambda <= 0) {
        throw std::invalid_argument("lambda must be greater than 0");
    }
    return 1 / lambda;
}

exponential_std()

double probability::geometric_dist::exponential_std

(

double

lambda

)

the standard deviation of the exponential distribution

Returns

\[\sigma = \frac{1}{\lambda}\]

Definition at line 59 of file exponential_dist.cpp.

                                      {
    if (lambda <= 0) {
        throw std::invalid_argument("lambda must be greater than 0");
    }
    return 1 / lambda;
}

exponential_var()

double probability::geometric_dist::exponential_var

(

double

lambda

)

the variance of the exponential distribution

Returns

\[\sigma^2 = \frac{1}{\lambda^2}\]

Definition at line 48 of file exponential_dist.cpp.

                                      {
    if (lambda <= 0) {
        throw std::invalid_argument("lambda must be greater than 0");
    }
    return 1 / pow(lambda, 2);
}

main()

int main

(

void

)

Main function.

Returns

0 on exit

Definition at line 148 of file exponential_dist.cpp.

           {
    test();  // Self test implementation
    return 0;
}

test()

static void test ( )

static

Self-test implementations.

Returns

void

Definition at line 72 of file exponential_dist.cpp.

                   {
    double lambda_1 = 1;
    double expected_1 = 1;
    double var_1 = 1;
    double std_1 = 1;
 
    double lambda_2 = 2;
    double expected_2 = 0.5;
    double var_2 = 0.25;
    double std_2 = 0.5;
 
    double lambda_3 = 3;
    double expected_3 = 0.333333;
    double var_3 = 0.111111;
    double std_3 = 0.333333;
 
    double lambda_4 = 0;     // Test 0
    double lambda_5 = -2.3;  // Test negative value
 
    const float threshold = 1e-3f;
 
    std::cout << "Test for lambda = 1 \n";
    assert(
        std::abs(expected_1 - probability::geometric_dist::exponential_expected(
                                  lambda_1)) < threshold);
    assert(std::abs(var_1 - probability::geometric_dist::exponential_var(
                                lambda_1)) < threshold);
    assert(std::abs(std_1 - probability::geometric_dist::exponential_std(
                                lambda_1)) < threshold);
    std::cout << "ALL TEST PASSED\n\n";
 
    std::cout << "Test for lambda = 2 \n";
    assert(
        std::abs(expected_2 - probability::geometric_dist::exponential_expected(
                                  lambda_2)) < threshold);
    assert(std::abs(var_2 - probability::geometric_dist::exponential_var(
                                lambda_2)) < threshold);
    assert(std::abs(std_2 - probability::geometric_dist::exponential_std(
                                lambda_2)) < threshold);
    std::cout << "ALL TEST PASSED\n\n";
 
    std::cout << "Test for lambda = 3 \n";
    assert(
        std::abs(expected_3 - probability::geometric_dist::exponential_expected(
                                  lambda_3)) < threshold);
    assert(std::abs(var_3 - probability::geometric_dist::exponential_var(
                                lambda_3)) < threshold);
    assert(std::abs(std_3 - probability::geometric_dist::exponential_std(
                                lambda_3)) < threshold);
    std::cout << "ALL TEST PASSED\n\n";
 
    std::cout << "Test for lambda = 0 \n";
    try {
        probability::geometric_dist::exponential_expected(lambda_4);
        probability::geometric_dist::exponential_var(lambda_4);
        probability::geometric_dist::exponential_std(lambda_4);
    } catch (std::invalid_argument& err) {
        assert(std::string(err.what()) == "lambda must be greater than 0");
    }
    std::cout << "ALL TEST PASSED\n\n";
 
    std::cout << "Test for lambda = -2.3 \n";
    try {
        probability::geometric_dist::exponential_expected(lambda_5);
        probability::geometric_dist::exponential_var(lambda_5);
        probability::geometric_dist::exponential_std(lambda_5);
    } catch (std::invalid_argument& err) {
        assert(std::string(err.what()) == "lambda must be greater than 0");
    }
    std::cout << "ALL TEST PASSED\n\n";
}