probability::geometric_dist::geometric_distribution Class Reference

A class to model the geometric distribution. More...

Public Member Functions
	geometric_distribution (const float &p)
	Constructor for the geometric distribution.
float	expected_value () const
	The expected value of a geometrically distributed random variable X.
float	variance () const
	The variance of a geometrically distributed random variable X.
float	standard_deviation () const
	The standard deviation of a geometrically distributed random variable X.
float	probability_density (const uint32_t &k) const
	The probability density function.
float	cumulative_distribution (const uint32_t &k) const
	The cumulative distribution function.
float	inverse_cumulative_distribution (const float &cdf) const
	The inverse cumulative distribution function.
uint32_t	draw_sample () const
	Generates a (discrete) sample according to the geometrical distribution.
float	range_tries (const uint32_t &min_tries=1, const uint32_t &max_tries=std::numeric_limits< uint32_t >::max()) const
	This function computes the probability to have success in a given range of tries.

Private Attributes
float	p
	The succes probability p.

Detailed Description

A class to model the geometric distribution.

Constructor & Destructor Documentation

geometric_distribution()

probability::geometric_dist::geometric_distribution::geometric_distribution ( const float & p )

inlineexplicit

Constructor for the geometric distribution.

Parameters

p	The success probability

: p(p) {}

Member Function Documentation

cumulative_distribution()

float probability::geometric_dist::geometric_distribution::cumulative_distribution ( const uint32_t & k ) const

inline

The cumulative distribution function.

The sum of all probabilities up to (and including) k trials. Basically CDF(k) = P(x <= k)

Parameters

k	The number of trials in [1,\infty)

Returns

The probability to have success within k trials

                                                           {
        return 1.0f - std::pow((1.0f - p), static_cast<float>(k));
    }

Here is the call graph for this function:

draw_sample()

uint32_t probability::geometric_dist::geometric_distribution::draw_sample ( ) const

inline

Generates a (discrete) sample according to the geometrical distribution.

Returns

A geometrically distributed number in [1,\infty)

                                 {
        float uniform_sample = generate_uniform();
        return static_cast<uint32_t>(
                   inverse_cumulative_distribution(uniform_sample)) +
               1;
    }

Here is the call graph for this function:

expected_value()

float probability::geometric_dist::geometric_distribution::expected_value ( ) const

inline

The expected value of a geometrically distributed random variable X.

Returns

E[X] = 1/p

{ return 1.0f / p; }

inverse_cumulative_distribution()

float probability::geometric_dist::geometric_distribution::inverse_cumulative_distribution ( const float & cdf ) const

inline

The inverse cumulative distribution function.

This functions answers the question: Up to how many trials are needed to have success with a probability of cdf? The exact floating point value is reported.

Parameters

cdf	The probability in [0,1]

Returns

The number of (exact) trials.

                                                                  {
        return std::log(1.0f - cdf) / std::log(1.0f - p);
    }

Here is the call graph for this function:

probability_density()

float probability::geometric_dist::geometric_distribution::probability_density ( const uint32_t & k ) const

inline

The probability density function.

As we use the first definition of the geometric series (1), we are doing k - 1 failed trials and the k-th trial is a success.

Parameters

k	The number of trials to observe the first success in [1,\infty)

Returns

A number between [0,1] according to p * (1-p)^{k-1}

                                                       {
        return std::pow((1.0f - p), static_cast<float>(k - 1)) * p;
    }

Here is the call graph for this function:

range_tries()

float probability::geometric_dist::geometric_distribution::range_tries ( const uint32_t & min_tries = 1, const uint32_t & max_tries = std::numeric_limits<uint32_t>::max() ) const

inline

This function computes the probability to have success in a given range of tries.

Computes P(min_tries <= x <= max_tries). Can be used to calculate P(x >= min_tries) by not passing a second argument. Can be used to calculate P(x <= max_tries) by passing 1 as the first argument

Parameters

min_tries	The minimum number of tries in [1,\infty) (inclusive)
max_tries	The maximum number of tries in [min_tries, \infty) (inclusive)

Returns

The probability of having success within a range of tries [min_tries, max_tries]

                                                                  {
        float cdf_lower = cumulative_distribution(min_tries - 1);
        float cdf_upper = max_tries == std::numeric_limits<uint32_t>::max()
                              ? 1.0f
                              : cumulative_distribution(max_tries);
        return cdf_upper - cdf_lower;
    }

Here is the call graph for this function:

standard_deviation()

float probability::geometric_dist::geometric_distribution::standard_deviation ( ) const

inline

The standard deviation of a geometrically distributed random variable X.

Returns

\sigma = \sqrt{V[X]}

{ return std::sqrt(variance()); }

Here is the call graph for this function:

variance()

float probability::geometric_dist::geometric_distribution::variance ( ) const

inline

The variance of a geometrically distributed random variable X.

Returns

V[X] = (1 - p) / p^2

{ return (1.0f - p) / (p * p); }

---

The documentation for this class was generated from the following file:

• probability/geometric_dist.cpp