< cpp‎ | numeric‎ | random
Pseudo-random number generation
Engines and engine adaptors
Uniform distributions
Bernoulli distributions
Poisson distributions
Normal distributions
Sampling distributions
Seed Sequences
C library
Defined in header <random>
template< class RealType = double >
class exponential_distribution;
(since C++11)

Produces random non-negative floating-point values x, distributed according to probability density function:

P(x|λ) = λe-λx

The value obtained is the time/distance until the next random event if random events occur at constant rate λ per unit of time/distance. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.

This is the continuous counterpart of std::geometric_distribution

std::exponential_distribution satisfies RandomNumberDistribution


[edit] Template parameters

RealType - The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

[edit] Member types

Member type Definition
result_type RealType
param_type the type of the parameter set, see RandomNumberDistribution.

[edit] Member functions

constructs new distribution
(public member function) [edit]
resets the internal state of the distribution
(public member function) [edit]
generates the next random number in the distribution
(public member function) [edit]
returns the lambda distribution parameter (rate of events)
(public member function) [edit]
gets or sets the distribution parameter object
(public member function) [edit]
returns the minimum potentially generated value
(public member function) [edit]
returns the maximum potentially generated value
(public member function) [edit]

[edit] Non-member functions

compares two distribution objects
(function) [edit]
performs stream input and output on pseudo-random number distribution
(function template) [edit]

[edit] Notes

Some implementations may occasionally return infinity if RealType is float. This is LWG issue 2524

[edit] Example

#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <random>
int main()
    std::random_device rd;
    std::mt19937 gen(rd());
    // if particles decay once per second on average,
    // how much time, in seconds, until the next one?
    std::exponential_distribution<> d(1);
    std::map<int, int> hist;
    for(int n=0; n<10000; ++n) {
    for(auto p : hist) {
        std::cout << std::fixed << std::setprecision(1) 
                  << p.first/2.0 << '-' << (p.first+1)/2.0 <<
                ' ' << std::string(p.second/200, '*') << '\n';

Possible output:

0.0-0.5 *******************
0.5-1.0 ***********
1.0-1.5 *******
1.5-2.0 ****
2.0-2.5 **
2.5-3.0 *

[edit] External links

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