std::extreme_value_distribution

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Pseudo-random number generation
Uniform random bit generators
Engines and engine adaptors
Non-deterministic generator
Distributions
Uniform distributions
Bernoulli distributions
Poisson distributions
extreme_value_distribution
(C++11)
Normal distributions
Sampling distributions
Seed Sequences
(C++11)
C library
 
 
Defined in header <random>
template< class RealType = double >
class extreme_value_distribution;
(since C++11)

Produces random numbers according to the extreme value distribution (it is also known as Gumbel Type I, log-Weibull, Fisher-Tippett Type I):

p(x;a,b) =
1
b
exp

a-x
b
- exp

a-x
b




std::extreme_value_distribution satisfies all requirements of 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(C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions

constructs new distribution
(public member function)
(C++11)
resets the internal state of the distribution
(public member function)
Generation
generates the next random number in the distribution
(public member function)
Characteristics
returns the distribution parameters
(public member function)
(C++11)
gets or sets the distribution parameter object
(public member function)
(C++11)
returns the minimum potentially generated value
(public member function)
(C++11)
returns the maximum potentially generated value
(public member function)

Non-member functions

(C++11)(C++11)(removed in C++20)
compares two distribution objects
(function)
performs stream input and output on pseudo-random number distribution
(function template)

Example

#include <random> 
#include <map>
#include <iomanip> 
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
 
template <int Height = 5, int BarWidth = 1, int Padding = 1, int Offset = 0, class Seq>
void draw_vbars(Seq&& s, const bool DrawMinMax = true) {
    static_assert((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
    auto cout_n = [](auto&& v, int n = 1) { while (n-- > 0) std::cout << v; };
    const auto [min, max] = std::minmax_element(std::cbegin(s), std::cend(s));
    std::vector<std::div_t> qr;
    for (typedef decltype(*cbegin(s)) V; V e : s)
        qr.push_back(std::div(std::lerp(V(0), Height*8, (e - *min)/(*max - *min)), 8));
    for (auto h{Height}; h-- > 0; cout_n('\n')) {
        cout_n(' ', Offset);
        for (auto dv : qr) {
            const auto q{dv.quot}, r{dv.rem};
            unsigned char d[] { 0xe2, 0x96, 0x88, 0 }; // Full Block: '█'
            q < h ? d[0] = ' ', d[1] = 0 : q == h ? d[2] -= (7 - r) : 0;
            cout_n(d, BarWidth), cout_n(' ', Padding);
        }
        if (DrawMinMax && Height > 1)
            Height - 1 == h ? std::cout << "┬ " << *max:
                          h ? std::cout << "│ "
                            : std::cout << "┴ " << *min;
    }
}
 
int main()
{
    std::random_device rd{};
    std::mt19937 gen{rd()};
 
    std::extreme_value_distribution<> d{-1.618f, 1.618f};
 
    const int norm = 10'000;
    const float cutoff = 0.000'3f;
 
    std::map<int, int> hist{};
    for(int n=0; n<norm; ++n) {
        ++hist[std::round(d(gen))];
    }
 
    std::vector<float> bars;
    std::vector<int> indices;
    for(const auto& [n,p] : hist) {
        float x = p*(1.0f/norm);
        if (x > cutoff) {
            bars.push_back(x);
            indices.push_back(n);
        }
    }
 
    draw_vbars<8,4>(bars);
 
    for (int n : indices) {
        std::cout << " " << std::setw(2) << n << "  ";
    }
    std::cout << '\n';
}

Possible output:

               ████ ▅▅▅▅                                                        ┬ 0.2186
               ████ ████                                                        │
          ▁▁▁▁ ████ ████ ▇▇▇▇                                                   │
          ████ ████ ████ ████                                                   │
          ████ ████ ████ ████ ▆▆▆▆                                              │
          ████ ████ ████ ████ ████ ▁▁▁▁                                         │
     ▄▄▄▄ ████ ████ ████ ████ ████ ████ ▃▃▃▃                                    │
▁▁▁▁ ████ ████ ████ ████ ████ ████ ████ ████ ▆▆▆▆ ▃▃▃▃ ▂▂▂▂ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ┴ 0.0005
 -5   -4   -3   -2   -1    0    1    2    3    4    5    6    7    8    9   10

External links

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