fj_xmax_approx.h File Reference

Two-moment approximation to the expected maximum of K i.i.d. More...

#include "line/api/fj/fj_gk_bound.h"
#include "line/api/fj/fj_harmonic.h"
#include "line/api/fj/fj_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for fj_xmax_approx.h:

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Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
FJXmaxApproxResult< T >	line::fj::fj_xmax_approx (unsigned K, const T &mu_X, const T &sigma_X, FJDistType type=FJDistType::Exp)
	Two-moment approximation to the expected maximum of K i.i.d.

Detailed Description

Two-moment approximation to the expected maximum of K i.i.d.

samples, X_K^max ~ mu_X + sigma_X G(K).

Templated port of matlab/src/api/fj/fj_xmax_approx.m, cross-checked against FJ_xmax.fj_xmax_approx in jar/src/main/java/jline/api/fj/FJ_xmax.java (identical).

MIXED ARITHMETIC. The exponential family uses G(K) = H_K - 1, which is rational and exact in any field; the uniform, EVD and bound families need sqrt or log and are only available when T carries transcendental functions. Asking for one of those at exact arithmetic throws UnsupportedError.

Definition in file fj_xmax_approx.h.