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<p>Weighted exponential distribution <i>WED</i> (<i>α, λ</i>) with shape parameter <i>α</i> and scale parameter <i>λ</i> possesses some good properties and can be used as a good fit to survival time data compared to other distributions such as gamma, Weibull, or generalized exponential distribution. In this article, we proved the existence and uniqueness of the maximum likelihood estimator (MLE) of the parameters of <i>WED</i> (<i>α, λ</i>) in simple random sampling (SRS) and provided explicit expressions for the Fisher information number in SRS. Moreover, we also proved the existence and uniqueness of the MLE of the parameters of <i>WED</i> (<i>α, λ</i>) in ranked set sampling (RSS) and provided explicit expressions for the Fisher information number in RSS. Simulation studies show that these MLEs in RSS can be real competitors for those in SRS.</p>

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Maximum likelihood estimation of the parameters of weighted exponential distribution in simple random sampling and ranked set sampling

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Cui-hong Deng,
  • Wang-xue Chen,
  • Ya-wen Zhou,
  • Rui Yang

摘要

Weighted exponential distribution WED (α, λ) with shape parameter α and scale parameter λ possesses some good properties and can be used as a good fit to survival time data compared to other distributions such as gamma, Weibull, or generalized exponential distribution. In this article, we proved the existence and uniqueness of the maximum likelihood estimator (MLE) of the parameters of WED (α, λ) in simple random sampling (SRS) and provided explicit expressions for the Fisher information number in SRS. Moreover, we also proved the existence and uniqueness of the MLE of the parameters of WED (α, λ) in ranked set sampling (RSS) and provided explicit expressions for the Fisher information number in RSS. Simulation studies show that these MLEs in RSS can be real competitors for those in SRS.