MLEBoot {LNPar}

Bootstrap standard errors for the estimators of a lognormal-Pareto mixture

Description

This function draws a bootstrap sample and uses it to estimate the parameters of a lognormal-Pareto mixture distribution. Since this is typically called by LPfit, see the help of LPfit for examples.

Usage

MLEBoot(x, y, minRank, p0, alpha0, mu0, Psi0)

Arguments

x

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

y

numerical vector: observed sample.

minRank

positive integer: minimum possible rank of the threshold.

p0

(0<p0<1): starting value of the mixing weight.

alpha0

non-negative scalar: starting value of the Pareto shape parameter.

mu0

scalar: starting value of the log-expectation of the lognormal distribution on the log scale.

Psi0

non-negative scalar: starting value of the log-variance of the lognormal distribution on the log scale.

Details

At each bootstrap replication, the mixture is estimated with thresholds equal to ys(minRank), ys(minRank+1),..., ys(n), where n is the sample size and ys is the sample in ascending order. The function is typically called by LPfit (see the example below).

Value

Estimated parameters obtained from a bootstrap sample.

References

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