snc_perc_backlog.h File Reference

Backlog quantile at a prescribed violation probability. More...

#include <cmath>
#include "line/api/snc/snc_thetaopt.h"
#include "line/api/snc/snc_types.h"
#include "line/util/error.h"

Include dependency graph for snc_perc_backlog.h:

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Namespaces
namespace	line
namespace	line::snc

Functions
SncResult	line::snc::snc_perc_backlog (const Envelope &arv, const Envelope &srv, double eps, double thetamax=1e3)
	Backlog quantile at a prescribed violation probability.

Detailed Description

Backlog quantile at a prescribed violation probability.

Inverts snc_bound_backlog in b: at fixed theta the smallest level for which the bound certifies P{B > b} <= eps is

b(theta) = sigmaA + sigmaS - log(eps*(1-exp(-theta*(rhoS-rhoA))))/theta,

and the reported quantile is its minimum over the feasible thetas. The minimizing theta differs from the one of the forward bound at a given level, which is why the inversion is done in closed form and re-optimized.

Port of matlab/src/api/snc/snc_perc_backlog.m.

Definition in file snc_perc_backlog.h.