Distribution of the time of attaining the maximum for the difference of the two Poisson's processes with negative linear drift

摘要

We are considering the combination of two Poisson processeswith linear drift on the whole real line in the case when negative middledrift is fulfilled. We find the distribution function for the moment ofattaining the maximum for this process. As well known frommonograph of Ibragimov and Khasminskii this distribution function isthe limit for the distributions of normalized maximum likelihoodestimators for the only discontinuous point of a density.