fj_xmax_moments_het.h File Reference

Moments of the maximum of heterogeneous exponentials by recurrence. More...

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

Include dependency graph for fj_xmax_moments_het.h:

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Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
std::vector< T >	line::fj::fj_xmax_moments_het (const std::vector< T > &lambda, unsigned n=1)
	Moments of the maximum of heterogeneous exponentials by recurrence.

Detailed Description

Moments of the maximum of heterogeneous exponentials by recurrence.

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

M_m(lambda, n) = [ n M_m(lambda, n-1)

• sum_{j=1..m} lambda_j M_{m-1}(lambda \ j, n) ] / sum_{j=1..m} lambda_j

with M_m(lambda, 0) = 1 and M_0(., n) = 0 for n >= 1, which is the n-th derivative of the transform recurrence of fj_lst_max_het at the origin.

Eq. (30) of the survey prints the second sum WITHOUT the lambda_j weight; that form is not the derivative of Eq. (29) and misses the textbook two-variable answer, so the weight is restored here. fj_xmax_het is the independent inclusion-exclusion check.

Definition in file fj_xmax_moments_het.h.