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.
We begin to study different limit theorems for order statistics. In this chapter we consider the asymptotic distributions for the so-called middle and intermediate order statistics.
Previous article Next article RecordsV. B. NevzorovV. B. Nevzorovhttps://doi.org/10.1137/1132032PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. Ahsanullah, Record values and the exponential distribution, Ann. Inst. Statist. Math., 30 (1978), 429–433 80h:62010 0444.62016 CrossrefGoogle Scholar[2] M. Ahsanullah, Characterization of the exponential distribution by record values, Sankhyā Ser. B, 41 (1979), 116–121 82f:62030 0517.62018 Google Scholar[3] M. Ahsanullah, Linear prediction of record values for the two-parameter exponential distribution, Ann. Inst. Statist. Math., 32 (1980), 363–368 82m:62105 0456.62026 CrossrefGoogle Scholar[4] M. Ahsanullah, On a characterization of the exponential distribution by weak homoscedasticity of record values, Biometrical J., 23 (1981), 715–717 84i:62016 0473.62015 CrossrefGoogle Scholar[5] Mohammad Ahsanullah, Record values of exponentially distributed random variables, Statist. 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