NAME¶

std::extreme_value_distribution - std::extreme_value_distribution

Synopsis¶

Defined in header <random>
template< class RealType = double > (since C++11)
class extreme_value_distribution;

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 constructs new distribution
(C++11) (public member function)
reset resets the internal state of the distribution
(C++11) (public member function)

Generation¶

operator() generates the next random number in the distribution
(C++11) (public member function)

Characteristics¶

a returns the distribution parameters
b (public member function)
param gets or sets the distribution parameter object
(C++11) (public member function)
min returns the minimum potentially generated value
(C++11) (public member function)
max returns the maximum potentially generated value
(C++11) (public member function)

Non-member functions¶

operator==
operator!= compares two distribution objects
(C++11) (function)
(C++11)(removed in C++20)
operator<< performs stream input and output on pseudo-random number
operator>> distribution
(C++11) (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.