fj_xmax_het.h File Reference

Exact moments of the maximum of heterogeneous exponentials. More...

#include <cstddef>
#include <vector>
#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>
T	line::fj::fj_xmax_het (const std::vector< T > &lambda, unsigned n=1)
	Exact moments of the maximum of heterogeneous exponentials.

Detailed Description

Exact moments of the maximum of heterogeneous exponentials.

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

E[Y^n] = sum over the nonempty subsets S of {1..K} of (-1)^(|S|+1) n! / ( sum_{i in S} lambda_i )^n

Exact, at a cost of 2^K - 1 terms. At n = 1 and K = 2 it collapses to 1/l1 + 1/l2 - 1/(l1+l2), and for equal rates to H_K/lambda.

Definition in file fj_xmax_het.h.