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Showing content from https://cplusplus.com/reference/random/exponential_distribution/ below:

class template

std::exponential_distribution

template <class RealType = double> class exponential_distribution;

Exponential distribution

Random number distribution that produces floating-point values according to an exponential distribution, which is described by the following probability density function:

This distribution produces random numbers where each value represents the interval between two random events that are independent but statistically defined by a constant average rate of occurrence (its lambda, λ).

The distribution parameter, lambda, is set on construction.

To produce a random value following this distribution, call its member function operator().

Its analogous discrete distribution is the geometric_distribution.

Template parameters

RealType: A floating-point type. Aliased as member type result_type.
By default, this is double.

Member types The following aliases are member types of geometric_distribution:

member type definition notes result_type The first template parameter (RealType) The type of the numbers generated (defaults to double) param_type not specified The type returned by member param.

Member functions

(constructor): Construct exponential distribution (public member function)

operator(): Generate random number (public member function)

reset: Reset distribution (public member function)

param: Distribution parameters (public member function)

min: Minimum value (public member function)

max: Maximum value (public member function)

Distribution parameters:

lambda: Lambda (public member function)

Non-member functions

operator<<: Insert into output stream (function template)

operator>>: Extract from input stream (function template)

relational operators: Relational operators (function template)

Example

// exponential_distribution
#include <iostream>
#include <random>

int main()
{
  const int nrolls=10000;  // number of experiments
  const int nstars=100;    // maximum number of stars to distribute
  const int nintervals=10; // number of intervals

  std::default_random_engine generator;
  std::exponential_distribution<double> distribution(3.5);

  int p[nintervals]={};

  for (int i=0; i<nrolls; ++i) {
    double number = distribution(generator);
    if (number<1.0) ++p[int(nintervals*number)];
  }

  std::cout << "exponential_distribution (3.5):" << std::endl;
  std::cout << std::fixed; std::cout.precision(1);

  for (int i=0; i<nintervals; ++i) {
    std::cout << float(i)/nintervals << "-" << float(i+1)/nintervals << ": ";
    std::cout << std::string(p[i]*nstars/nrolls,'*') << std::endl;
  }

  return 0;
}

Possible output:

exponential_distribution (3.5):
0.0-0.1: *****************************
0.1-0.2: *********************
0.2-0.3: **************
0.3-0.4: *********
0.4-0.5: *******
0.5-0.6: *****
0.6-0.7: ***
0.7-0.8: **
0.8-0.9: *
0.9-1.0: *