fj_xmax_emma.h File Reference

EMMA (Extreme-value Maximum Moment Approximation) to the expected maximum of K i.i.d. More...

#include <functional>
#include "line/api/fj/fj_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for fj_xmax_emma.h:

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Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
T	line::fj::fj_xmax_emma (unsigned K, const T &mu)
	Exponential branch.
template<class T>
T	line::fj::fj_xmax_emma (unsigned K, const std::function< T(const T &)> &Finv)
	General branch: the caller supplies the quantile function F^{-1}.

Detailed Description

EMMA (Extreme-value Maximum Moment Approximation) to the expected maximum of K i.i.d.

samples.

Templated port of matlab/src/api/fj/fj_xmax_emma.m, cross-checked against FJ_xmax.fj_xmax_emma in jar/src/main/java/jline/api/fj/FJ_xmax.java (identical; both use the same rounded constant phi = 0.570376, which is exp(-exp(-gamma)) to six places).

exponential: E[Y_K] = -(1/mu) ln(1 - phi^{1/K}) general: E[Y_K] = F^{-1}(phi^{1/K})

static_assert(num_traits<T>::has_transcendental) – a real root phi^{1/K} and a log. The general form takes the quantile function as a callable, so the caller supplies whatever inverse CDF it has.

Definition in file fj_xmax_emma.h.