geometric_dist.cpp File Reference

Geometric Distribution More...

#include <cassert>
#include <cmath>
#include <cstdint>
#include <ctime>
#include <iostream>
#include <limits>
#include <random>
#include <vector>

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Classes
class	probability::geometric_dist::geometric_distribution
	A class to model the geometric distribution. More...

Namespaces
namespace	probability
	Probability algorithms.
namespace	geometric_dist
	Functions for the Geometric Distribution algorithm implementation.

Functions
float	probability::geometric_dist::generate_uniform ()
	Returns a random number between [0,1]. More...
void	sample_test (const probability::geometric_dist::geometric_distribution &dist)
	Tests the sampling method of the geometric distribution. More...
static void	test ()
	Self-test implementations. More...
int	main ()
	Main function. More...

Detailed Description

Geometric Distribution

The geometric distribution models the experiment of doing Bernoulli trials until a sucess was observed. There are two formulations of the geometric distribution: 1) The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ... } 2) The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... } Here, the first one is implemented.

Common variables used: p - The success probability k - The number of tries

Author

Domenic Zingsheim

Function Documentation

generate_uniform()

float probability::geometric_dist::generate_uniform

(

)

Returns a random number between [0,1].

Returns

A uniformly distributed random number between 0 (included) and 1 (included)

                         {
    return static_cast<float>(rand()) / static_cast<float>(RAND_MAX);
}

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main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    srand(time(nullptr));
    test();  // run self-test implementations
    return 0;
}

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sample_test()

void sample_test

(

const probability::geometric_dist::geometric_distribution &

dist

)

Tests the sampling method of the geometric distribution.

Draws 1000000 random samples and estimates mean and variance These should be close to the expected value and variance of the given distribution to pass.

Parameters

dist	The distribution to test

                                                                              {
    uint32_t n_tries = 1000000;
    std::vector<float> tries;
    tries.resize(n_tries);
 
    float mean = 0.0f;
    for (uint32_t i = 0; i < n_tries; ++i) {
        tries[i] = static_cast<float>(dist.draw_sample());
        mean += tries[i];
    }
 
    mean /= static_cast<float>(n_tries);
 
    float var = 0.0f;
    for (uint32_t i = 0; i < n_tries; ++i) {
        var += (tries[i] - mean) * (tries[i] - mean);
    }
 
    //Unbiased estimate of variance
    var /= static_cast<float>(n_tries - 1);
 
    std::cout << "This value should be near " << dist.expected_value() << ": " << mean << std::endl;
    std::cout << "This value should be near " << dist.variance() << ": " << var << std::endl;
}

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test()

static void test ( )

static

Self-test implementations.

Returns

void

                   {
    probability::geometric_dist::geometric_distribution dist(0.3);
 
    const float threshold = 1e-3f;
 
    std::cout << "Starting tests for p = 0.3..." << std::endl;
    assert(std::abs(dist.expected_value() - 3.33333333f) < threshold);
    assert(std::abs(dist.variance() - 7.77777777f) < threshold);
    assert(std::abs(dist.standard_deviation() - 2.788866755) < threshold);
    assert(std::abs(dist.probability_density(5) - 0.07203) < threshold);
    assert(std::abs(dist.cumulative_distribution(6) - 0.882351) < threshold);
    assert(std::abs(dist.inverse_cumulative_distribution(dist.cumulative_distribution(8)) - 8) < threshold);
    assert(std::abs(dist.range_tries() - 1.0f) < threshold);
    assert(std::abs(dist.range_tries(3) - 0.49f) < threshold);
    assert(std::abs(dist.range_tries(5, 11) - 0.2203267f) < threshold);
    std::cout << "All tests passed" << std::endl;
    sample_test(dist);
 
    dist = probability::geometric_dist::geometric_distribution(0.5f);
 
    std::cout << "Starting tests for p = 0.5..." << std::endl;
    assert(std::abs(dist.expected_value() - 2.0f) < threshold);
    assert(std::abs(dist.variance() - 2.0f) < threshold);
    assert(std::abs(dist.standard_deviation() - 1.4142135f) < threshold);
    assert(std::abs(dist.probability_density(5) - 0.03125) < threshold);
    assert(std::abs(dist.cumulative_distribution(6) - 0.984375) < threshold);
    assert(std::abs(dist.inverse_cumulative_distribution(dist.cumulative_distribution(8)) - 8) < threshold);
    assert(std::abs(dist.range_tries() - 1.0f) < threshold);
    assert(std::abs(dist.range_tries(3) - 0.25f) < threshold);
    assert(std::abs(dist.range_tries(5, 11) - 0.062011f) < threshold);
    std::cout << "All tests passed" << std::endl;
    sample_test(dist);
 
    dist = probability::geometric_dist::geometric_distribution(0.8f);
 
    std::cout << "Starting tests for p = 0.8..." << std::endl;
    assert(std::abs(dist.expected_value() - 1.25f) < threshold);
    assert(std::abs(dist.variance() - 0.3125f) < threshold);
    assert(std::abs(dist.standard_deviation() - 0.559016f) < threshold);
    assert(std::abs(dist.probability_density(5) - 0.00128) < threshold);
    assert(std::abs(dist.cumulative_distribution(6) - 0.999936) < threshold);
    assert(std::abs(dist.inverse_cumulative_distribution(dist.cumulative_distribution(8)) - 8) < threshold);
    assert(std::abs(dist.range_tries() - 1.0f) < threshold);
    assert(std::abs(dist.range_tries(3) - 0.04f) < threshold);
    assert(std::abs(dist.range_tries(5, 11) - 0.00159997f) < threshold);
    std::cout << "All tests have successfully passed!" << std::endl;
    sample_test(dist);
}

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