A hazard rate λ(t) is assumed to be of the shape of the “first” part of a “bathtub” model, i.e., λ(t) is non-increasing for t < τ and is constant for t ≥ τ . The isotonic maximum likelihood estimator of the hazard rate is obtained and its asymptotic distribution is investigated. This leads to the maximum likelihood estimator and a confidence interval for a new version of the change point parame...

In this paper, we propose new asymptotic confidence intervals for extreme quantiles, that is, quantiles located outside the range of available data. We restrict ourselves to situation where underlying distribution is heavy-tailed. While are mostly constructed around a pivotal quantity, consider here an alternative approach based on order statistics sampled from uniform distribution. The converg...