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 Generalized 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 (C++11) 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
(C++11)
 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 <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <vector>
 
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(0 < Height and 0 < BarWidth and 0 <= Padding and 0 <= Offset);
 
    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(*std::cbegin(s)) V; V e : s)
        qr.push_back(std::div(std::lerp(V(0), 8 * Height,
                                        (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)
        if (const float x = p * (1.0f / norm); 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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