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Showing content from https://en.cppreference.com/w/cpp/algorithm/../numeric/random/exponential_distribution.html below:

std::exponential_distribution - cppreference.com

template< class RealType = double >
class exponential_distribution;

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

\(\small P(x|\lambda) = \lambda e^{-\lambda x}\)P(x|λ) = λe-λx

The value obtained is the time/distance until the next random event if random events occur at constant rate \(\small\lambda\)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.

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

#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
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)
        ++hist[2 * d(gen)];
 
    for (auto const& [x, y] : hist)
        std::cout << std::fixed << std::setprecision(1)
                  << x / 2.0 << '-' << (x + 1) / 2.0 << ' '
                  << std::string(y / 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 *
3.0-3.5
3.5-4.0

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