LAUSR

Abstract This study makes a new contribution to extreme value theory by proposing a change-point model of the distribution of the r-larger order statistics. In some situations, using only the maxima of grouped data results in a small sample size that may require a larger dataset. In this sense, using the joint distribution of the r-largest order statistics provides more information and, consequently, better estimators. We perform a comprehensive simulation to show the advantage of this method over other competitive models that approach the change-point model in extremes. Finally, the proposed model is fitted to river quota data (environmental data) and NASDAQ daily returns data (financial data) to demonstrate its potential for practical application.