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<p>We present sharp lower and upper bounds on the variances of generalized order statistics with arbitrarily fixed model parameters valid for arbitrary baseline distributions with finite second moments. The bounds are expresssed with use of the scale units being the variances of baseline distributions. Special cases of submodels are discussed. Moreover, explicit formulae for the density and distribution functions of generalized order statistics are presented.</p>

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Sharp bounds on variances of generalized order statistics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月24日

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  • Tomasz Rychlik

摘要

We present sharp lower and upper bounds on the variances of generalized order statistics with arbitrarily fixed model parameters valid for arbitrary baseline distributions with finite second moments. The bounds are expresssed with use of the scale units being the variances of baseline distributions. Special cases of submodels are discussed. Moreover, explicit formulae for the density and distribution functions of generalized order statistics are presented.