# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.evt.evd.univariate.fitting.acer

## Class ACERFunction

• All Implemented Interfaces:
Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction

public class ACERFunction
extends AbstractUnivariateRealFunction
The ACER (Average Conditional Exceedance Rate) function $$\epsilon_k(\eta)$$ approximates the probability $\epsilon_k(\eta) = Pr(X_k > \eta | X_1 \le \eta, X_2 \le \eta, ..., X_{k-1} \le \eta)$ for a sequence of stochastic process observations $$X_i$$ with a k-step memory.

The function is of the form (Gumbel-type): $\hat{\epsilon_k}(\eta) = q_k exp(-a_k (\eta - b_k)^{c_k}), \eta \ge \eta_1$

The R equivalent function is acer::acer.evaluate. Note: R defines the conditional of epsilon using "less than" but this implementation sticks to the original paper which uses "less than or equal to".

eta - the barrier level $$\eta$$