LRExp {Renext}

Likelihood Ratio statistic for exponential vs. GPD

Description

Likelihood Ratio statistic for the exponential distribution vs. GPD.

Usage

   LRExp(x, alternative = c("lomax", "GPD", "gpd", "maxlo"))

Arguments

x

Numeric vector of positive sample values. For the POT context, this should be the vector of excesses over the threshold.

alternative

Character string describing the alternative hypothesis

Details

The Likelihood-Ratio statistic is actually W:=-2 \log \textrm{LR} where LR is the ratio of the likelihoods exponential to alternative distribution.

Value

The LR statistic value.

Note

When the alternative is "lomax" or "maxlo", the statistic has a distribution of mixed type under the null hypothesis of exponentiality. This is a mixture of a distribution of continuous type (with positive values) and of a Dirac mass at LR = 0. The probability mass \textrm{Pr}\{\textrm{LR} = 0\} can be computed using the pGreenwood1 function. More precisely, the probability mass is pGreenwood1(n) for the Lomax alternative and 1.0 - pGreenwood1(n) for the maxlo alternative, where n is the sample size length(x).

See Also

LRExp.test for the related LR test of exponentiality.