On Estimation of Weibull-Tail and Log-Weibull-tail Distributions for Modeling End-to-end Delay

We model the distribution tails of the end-to-end delay of services with the help of two-parameter Weibull-tail and log-Weibull-tail distributions. First we discuss the role of the Weibull-tail and log-Weibull-tail distributions in statistics of extremes. Then we propose the statistical procedure based on the largest observations of a sample to decide between these two tail models and to estimate the parameters of the selected model. The proposed procedure allows us to estimate the extreme quantiles from theWeibull-tail and log-Weibull-tail distributions in an unified way. The efficiency of the introduced methods is illustrated on a small simulation study.