Almost sure local central limit theorem for sample range

Qing-Pei Zang

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1050-1055

Abstract: Let {Xn; n ⩾ 1} be a sequence of independent and identically distributed random variables. The sample range is Rn=max1≤i≤nXi-min1≤i≤nXi$R_{n}=\max \nolimits _{1\le i\le n}X_{i}-\min \nolimits _{1\le i\le n}X_{i}$. In this paper, we derive, under some mild assumptions, an almost sure local central limit theorem for sample range.

Date: 2017
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DOI: 10.1080/03610926.2012.763092

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