An order statistics model based on the list of top m scores after lth change

摘要

Consider an infinite sequence of independent identically distributed (i.i.d.) continuous random variables. We begin with an initial set of m random variables and keep in our list only the top m values as new variables are observed sequentially and added to the data set. We obtain the joint distribution of the ordered observations in our list after the lth change occurs to the list. We also obtain the probability of a change in the list given that there are already l changes. We discuss the relationship between the proposed model, ordinary order statistics, and m-records.