std::extreme_value_distribution

 

C++

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Pseudo-random number generation

Uniform random bit generators   uniform_random_bit_generator (C++20) Random number engines linear_congruential_engine (C++11) mersenne_twister_engine (C++11) subtract_with_carry_engine (C++11) philox_engine (C++26) Random number engine adaptors discard_block_engine (C++11) independent_bits_engine (C++11) shuffle_order_engine (C++11) Predefined random number generators Non-deterministic random numbers random_device (C++11) Utilities generate_canonical (C++11) seed_seq (C++11) Random number algorithms ranges::generate_random (C++26) C random library rand    srand    RAND_MAX

Random number distributions Uniform distributions uniform_int_distribution (C++11) uniform_real_distribution (C++11) generate_canonical (C++11) Bernoulli distributions bernoulli_distribution (C++11) binomial_distribution (C++11) negative_binomial_distribution (C++11) geometric_distribution (C++11) Poisson distributions poisson_distribution (C++11) exponential_distribution (C++11) gamma_distribution (C++11) weibull_distribution (C++11) extreme_value_distribution (C++11) Normal distributions normal_distribution (C++11) lognormal_distribution (C++11) chi_squared_distribution (C++11) cauchy_distribution (C++11) fisher_f_distribution (C++11) student_t_distribution (C++11) Sampling distributions discrete_distribution (C++11) piecewise_constant_distribution (C++11) piecewise_linear_distribution (C++11)

 

std::extreme_value_distribution

Member functions

extreme_value_distribution::extreme_value_distribution

extreme_value_distribution::reset

Generation

extreme_value_distribution::operator()

Characteristics

extreme_value_distribution::aextreme_value_distribution::b

extreme_value_distribution::param

extreme_value_distribution::min

extreme_value_distribution::max

Non-member functions

operator==operator!= (C++11)(C++11)(until C++20)

operator<<operator>> (C++11)(C++11)

 

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):

\({\small p(x;a,b) = \frac{1}{b} \exp{(\frac{a-x}{b}-\exp{(\frac{a-x}{b})})} }\)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

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

Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20)	compares two distribution objects (function)
operator<<operator>> (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,
         bool MinMax = true, class S>
void draw_vbars(S const& s)
{
    static_assert((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
 
    const auto repeat_cout = [](auto const& v, int n)
    {
        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 (float e : s) {
        qr.push_back(std::div(std::lerp(0.f, Height * 8 , (e - *min) / (*max - *min)), 8));
    }
    for (auto h{Height}; h-- > 0 ;) {
        repeat_cout(' ', Offset);
        for (auto [q, r] : qr) {
            char d[] = "█"; // == { 0xe2, 0x96, 0x88, 0 }
            if (q < h) {
                repeat_cout(' ', BarWidth);
            } else {
                if (q == h) {
                    d[2] -= (7 - r);
                }
                repeat_cout(d, BarWidth);
            }
            repeat_cout(' ', Padding);
        }
        if (MinMax && Height > 1) {
            std::cout << "│";
            if (h == Height - 1) std::cout << " " << *max;
            else if (h == 0) std::cout << " " << *min;
        }
        std::cout << '\n';
    }
}
 
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:

               ████ ▂▂▂▂                                                        │ 0.2227
               ████ ████                                                        │
               ████ ████ ▆▆▆▆                                                   │
          ████ ████ ████ ████                                                   │
          ████ ████ ████ ████ ▅▅▅▅                                              │
          ████ ████ ████ ████ ████ ▂▂▂▂                                         │
     ▄▄▄▄ ████ ████ ████ ████ ████ ████ ▂▂▂▂                                    │
▁▁▁▁ ████ ████ ████ ████ ████ ████ ████ ████ ▆▆▆▆ ▃▃▃▃ ▂▂▂▂ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ │ 0.0006
 
 -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.