Some results on maximum of expected sums of sequential minima

V. B. Nevzorov and A. Stepanov

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 6, 1362-1369

Abstract: Let X1,…,Xn be independent and identically distributed continuous nonnegative random variables and mn be the sample minimum. In the present paper, we propose an approach, which maximizes the value E(∑i=knmin{Xi,…,Xn}) and makes it greater than E(∑i=1nmi|X1=x1,…,Xk−1=xk−1). We further apply this approach to the standard uniform and exponential distributions and for finding the corresponding values x1,…,xk−1 solve proper algebraic equations by numerical methods.

Date: 2021
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DOI: 10.1080/03610926.2019.1649431

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