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WOS: 000463698900009, Assume that only the lists of upper k-records and lower k-records of a finite sequence are available and the existence of a monotonic trend in location is interested in. In this study, a distribution-free test based on the difference between the numbers of upper and lower k-records is proposed for this situation. The exact and asymptotic distributions of the proposed test statistic are obtained for a random continuous sequence which is independent and identically distributed (i.i.d.). Also, a comparison between the proposed test and some well-known distribution-free tests is made in terms of empirical powers.

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.