Bottom-k-Lists

Abstract

Consider an infinite sequence of iid continuous random variables. In this paper, we introduce duals of top-k-lists which is called ”Bottom-k-lists”. We also derive the joint probability density function (pdf) of the ordered elements of `th bottom-k-list and its relation with the joint pdf of dual (lower) generalized order statistics (dGOS). In addition, we give a distributional relation between each element of l-th bottom-k-list, ordinary order statistics (oOS), and lower k-records.

Keywords

• Lower k-records,Bottom-k-lists,Dual generalized order statistics,Meijer’s G function,Ordinary order statistics

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