fj_xmax_normal.h File Reference

Expected maximum and variance of K i.i.d. More...

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

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Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
FJXmaxNormalResult< T >	line::fj::fj_xmax_normal (unsigned K, const T &mu, const T &sigma, FJNormalMethod method=FJNormalMethod::Johnson)
	Expected maximum and variance of K i.i.d.

Detailed Description

Expected maximum and variance of K i.i.d.

normal samples.

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

arnold: G(K) = sqrt(2 ln K) johnson: G(K) = sqrt(2 ln K) - (ln ln K - ln(4 pi) + 2 gamma)/(2 sqrt(2 ln K)) corrected: johnson minus the Petzold bias 0.1727 K^-0.2750 Var ~ 1.64492 sigma^2 / (2 ln K)

static_assert(num_traits<T>::has_transcendental) – log, sqrt and a real power throughout. Note ln ln K is -inf at K = 2 in MATLAB (ln 2 < 1 makes ln ln K finite and negative; it is K = 1 that diverges), and the function requires K >= 2 for that reason.

Definition in file fj_xmax_normal.h.