< cpp‎ | numeric‎ | random
Pseudo-random number generation
Uniform random bit generators
Engines and engine adaptors
Non-deterministic generator
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

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.

Member types

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

Member functions

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

Non-member functions

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


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


#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 *

External links

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