Hypothesis testing for a L\'evy-driven storage system by Poisson sampling
Probability
2020-11-23 v2 Statistics Theory
Statistics Theory
Abstract
This paper focuses on hypothesis testing for the input of a L\'evy-driven storage system by sampling of the storage level. As the likelihood is not explicit we propose two tests that rely on transformation of the data. The first approach uses i.i.d. `quasi-busy-periods' between observations of zero workload. The distribution of the duration of quasi-busy-periods is determined. The second method is a conditional likelihood ratio test based on the Bernoulli events of observing a zero or positive workload, conditional on the previous workload. Performance analysis is presented for both tests along with speed-of-convergence results, that are of independent interest.
Cite
@article{arxiv.1912.02891,
title = {Hypothesis testing for a L\'evy-driven storage system by Poisson sampling},
author = {Michel Mandjes and Liron Ravner},
journal= {arXiv preprint arXiv:1912.02891},
year = {2020}
}