Exact strong laws of large numbers for ratios of the smallest order statistics

Przemysław Matuła, Paweł Kurasiński and André Adler

Statistics & Probability Letters, 2019, vol. 152, issue C, 69-73

Abstract: Let Xn,kn∈N,1≤k≤kn be an array of independent and identically distributed random variables. We take the smallest order statistics Xn,(1) and Xn,(2) in each row and consider the ratios Rn=Xn,(2)∕Xn,(1). Then we study the almost sure convergence of weighted sums of these ratios in two cases: kn→∞ and when kn=K is fixed. Our theorems are proved under very mild conditions and they extend the results of all the papers on this topic that only explored the uniform, exponential and Pareto distributions.

Keywords: Strong law of large numbers; i.i.d. random variables; Order statistics (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2019.04.014

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