# std::geometric_distribution

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< cpp‎ | numeric‎ | random

Defined in header `<random>` |  |
template< class IntType = int > class geometric_distribution; |  | (since C++11)

Produces random non-negative integer values i, distributed according to discrete probability function:

  \(P(i|p) = p \cdot (1-p)^i\)P(i|p) = p · (1 − p)i

The value represents the number of yes/no trials (each succeeding with probability p) which are necessary to obtain a single success.

`std::geometric_distribution<>(p)` is exactly equivalent to std::negative_binomial_distribution<>(1, p). It is also the discrete counterpart of std::exponential_distribution.

`std::geometric_distribution` satisfies RandomNumberDistribution

### Template parameters

IntType | - | The result type generated by the generator. The effect is undefined if this is not one of short, int, long, long long, unsigned short, unsigned int, unsigned long, or unsigned long long.

### Member types

Member type | Definition
`result_type` | IntType
`param_type` | the type of the parameter set, see RandomNumberDistribution.

### Member functions

(constructor) | constructs new distribution (public member function)
reset | resets the internal state of the distribution (public member function)

##### Generation

operator() | generates the next random number in the distribution (public member function)

##### Characteristics

p | returns the p distribution parameter (probability of a trial generating true) (public member function)
param | gets or sets the distribution parameter object (public member function)
min | returns the minimum potentially generated value (public member function)
max | returns the maximum potentially generated value (public member function)

### Non-member functions

operator==operator!= | compares two distribution objects (function)
operator<<operator>> | performs stream input and output on pseudo-random number distribution (function template)

### Example

geometric_distribution<>(0.5) is the default and represents the number of coin tosses that are required to get heads

Run this code

    #include <iostream>
    #include <iomanip>
    #include <string>
    #include <map>
    #include <random>
    int main()
    {
        std::random_device rd;
        std::mt19937 gen(rd());

        std::geometric_distribution<> d; // same as std::negative_binomial_distribution<> d(1, 0.5);

        std::map<int, int> hist;
        for(int n=0; n<10000; ++n) {
            ++hist[d(gen)];
        }
        for(auto p : hist) {
            std::cout << p.first <<
                    ' ' << std::string(p.second/100, '*') << '\n';
        }
    }

Output:

    0 *************************************************
    1 *************************
    2 ************
    3 ******
    4 **
    5 *
    6
    7
    8
    9
    10
    11

### External links

Weisstein, Eric W. "Geometric Distribution." From MathWorld--A Wolfram Web Resource.

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