Hypothesis testing for a L\'evy-driven storage system by Poisson sampling

TL;DR

This paper develops two novel hypothesis tests for analyzing the input process of a Le9vy-driven storage system using sampled workload data, with performance analysis and convergence results.

Contribution

It introduces two data transformation-based tests for Le9vy-driven systems where likelihood is intractable, advancing statistical inference methods in this context.

Findings

Distribution of quasi-busy-periods is explicitly determined

Performance and convergence of tests are rigorously analyzed

Tests are effective for hypothesis testing in Le9vy-driven storage systems

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.