LPtest {LNPar}

Testing for a Pareto tail

Description

This function draws a bootstrap sample from the null (lognormal) distribution and computes the test for the null hypothesis of a pure lognormal distribution versus the alternative of a lognormal-Pareto mixture. To be only called from ParallelTest.

Usage

LPtest(x, n, muNull, sigmaNull, minRank)

Arguments

x

list: sequence of integers 1,...,K, where K is the mumber of datasets. Set x = 1 in case of a single dataset.

n

sample size.

muNull

lognormal expected value under the null hypothesis.

sigmaNull

lognormal standard deviation under the null hypothesis.

minRank

minimum possible rank of the threshold.

Value

A list with the following elements:

LR: observed value of the llr test.

References

Bee M (2022). “On discriminating between lognormal and Pareto tail: an unsupervised mixture-based approach.” Advances in Data Analysis and Classification. doi:10.1007/s11634-022-00497-4.

Examples

n = 100
muNull = mean(log(TN2016))
sigmaNull = sd(log(TN2016))
minRank = 90
res = LPtest(1,n,muNull,sigmaNull,minRank)