std::extreme_value_distribution

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C library
 
std::extreme_value_distribution
 
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

(C++11)
 constructs new distribution
(public member function)
(C++11)
 resets the internal state of the distribution
(public member function)
Generation
(C++11)
 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)
(C++11)
 performs stream input and output on pseudo-random number distribution
(function template)

Example

Run this code
#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.

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