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<p>The joint or marginal distribution of order statistics is complicated in general, but it has a unified formula for continuous random samples. For simplicity, almost all statistical textbooks and monographs only introduce and prove some of its special forms. Thus, we give a unified proof of the general form, which is much simpler than existing proofs in statistical literature.</p>

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Simple and unified proof of the joint or marginal density function of order statistics

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Jin Zhang

摘要

The joint or marginal distribution of order statistics is complicated in general, but it has a unified formula for continuous random samples. For simplicity, almost all statistical textbooks and monographs only introduce and prove some of its special forms. Thus, we give a unified proof of the general form, which is much simpler than existing proofs in statistical literature.