Likelihood Ratio statistic for exponential vs. GPD

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

Value

The LR statistic value.

Details

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

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.