Title: Bounds for CDFs of Order Statistics Arising from INID Random Variables
Abstract:In recent decades, studying order statistics arising from independent and not necessary identically distributed (INID) random variables has been a remarkable concern for researchers.The cumulative dis...In recent decades, studying order statistics arising from independent and not necessary identically distributed (INID) random variables has been a remarkable concern for researchers.The cumulative distribution function (CDF) of these random variables (F i:n ) is a complex manipulating, long time consuming and a softwareintensive tool that takes considerable time.Therefore, obtain approximations and bounds for F i:n and other theoretical properties of these variables, such as moments, quantiles, characteristic functions, and some related probabilities, has always been the main challenge.Recently, Bayramoglu (2018), Bayramoglu (2018), has introduced a set of CDFs (F [i] ), whose definitions are based on a point to point ordering of the original CDFs (F i ), that can be used to approximate the CDF of i-th order statistics (F i:n ).Here, by using just F [1] and F [n] , we provide new upper and lower bounds for the F i:n .Furthermore, new approximations for F 1:n and F n:n , as well as for other cases, are derived.Comparisons with respect to approximations suggested by Bayramoglu Bayramoglu (2018) are also provided.Read More