Adaptive hazard estimator of the peak over threshold model under random censoring with application

Although the hazard rates sharing a number of similar aspects. The hazard functions are far less frequently used. The problem of hazard functions estimation has received much attention in the statistical literature. This paper studies the hazard rate estimation with the peak over threshold (POT) modeling within completed data. Next, we have to adapt this estimation with the censored data. Ditto, the asymptotic normality has been established, whereas the case of random threshold t under the uncensored and the censored data, In this dissertation, our procedure of our asymptotic result is based on POT context with the threshold t is random. Wherefore we study the asymptotic normality of the proportion of non-censored observation estimator with the threshold t is random. As an application, we present a new extreme value index (EVI) in terms of the hazard functions estimation with both full and censored data. Then, we establish the asymptotic normality of the new EVI estimator for the heavy tailed index associated with the hazard function without censored for POT. And we adapted this estimator index with censored data for POT where the threshold t is random.