A GENERALIZED VERSION OF FOSTER AND STUARTíS d-STATISTIC

Abstract

Assume that only the lists of upper k-records and lower k-recordsof a Önite sequence are available and the existence of a monotonic trend inlocation is interested in. In this study, a distribution-free test based on thedi§erence between the numbers of upper and lower k-records is proposed forthis situation. The exact and asymptotic distributions of the proposed teststatistic are obtained for a random continuous sequence which is independentand identically distributed (i.i.d.). Also, a comparison between the proposedtest and some well-known distribution-free tests is made in terms of empiricalpowers.