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<p>This study investigates the problem of testing the equality of two population distributions when one sample is obtained through independent random sampling and the other through a design-based biased mechanism. Motivating examples, such as tree diameter data from forest inventory, highlight the practical relevance of this setting. To address the challenge, we develop a graphical diagnostic tool and formal hypothesis tests within the framework of weighted distributions. A Monte Carlo simulation study is used to assess the performance of the proposed methods in terms of size control and power. Finally, the methodology is demonstrated on diameter-at-breast-height data from the Pertouli Forest (Greece), using random and size-biased samples from hybrid fir to validate the method under a known common population, and a further comparison with a random black pine sample to illustrate its behavior when population equivalence is known not to hold.</p>

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Two-sample problem using a random and a biased sample

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月17日

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  • Apostolos Batsidis,
  • Aristeidis Georgakis,
  • Polychronis Economou

摘要

This study investigates the problem of testing the equality of two population distributions when one sample is obtained through independent random sampling and the other through a design-based biased mechanism. Motivating examples, such as tree diameter data from forest inventory, highlight the practical relevance of this setting. To address the challenge, we develop a graphical diagnostic tool and formal hypothesis tests within the framework of weighted distributions. A Monte Carlo simulation study is used to assess the performance of the proposed methods in terms of size control and power. Finally, the methodology is demonstrated on diameter-at-breast-height data from the Pertouli Forest (Greece), using random and size-biased samples from hybrid fir to validate the method under a known common population, and a further comparison with a random black pine sample to illustrate its behavior when population equivalence is known not to hold.