fj_xmax_hz.h File Reference

Harrison-Zertal approximation of the maximum of i.i.d. More...

#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_hz.h:

Go to the source code of this file.

Classes
struct	line::fj::FJXmaxHzResult< T >
	[Xmax, resid] of fj_xmax_hz. More...

Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
FJXmaxHzResult< T >	line::fj::fj_xmax_hz (const T &m1, const T &m2, unsigned K)
	Harrison-Zertal approximation of the maximum of i.i.d.

Detailed Description

Harrison-Zertal approximation of the maximum of i.i.d.

variables.

Templated port of matlab/src/api/fj/fj_xmax_hz.m.

X_K^max ~ m1 + ( m2 / (2 m1) ) ( H_K - 1 )

The correction is the equilibrium mean of the branch law scaled by H_K - 1: one branch, plus the residual work still owed by the branches that finish later. Writing m2/(2 m1) = m1 (1+SCV)/2 shows it is exact for the exponential and reduces to m1 at K = 1 for every branch law.

Definition in file fj_xmax_hz.h.