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<p>The existence and uniqueness of the maximum likelihood estimator (MLE) of parameter for the exponential-Poisson distribution is discussed by Kuş [2007. A new lifetime distribution. Computational Statistics and Data Analysis 51(9): 4497–4509] in simple random sampling (SRS). As an alternative to the MLEs in SRS, Joukar et al. [2021. Parameter estimation for the exponential-poisson distribution based on ranked set samples. Communication in Statistics-Theory and Methods 50(3): 560–581] discussed the MLE of parameter for this distribution in ranked set sampling (RSS). However, they did not discuss the existence and uniqueness of the MLE in RSS and did not provide explicit expressions for the Fisher information in RSS. In this article, we discuss the existence and uniqueness of the MLE of parameter in RSS and give explicit expressions for the Fisher information in RSS. The MLEs will be compared in terms of asymptotic efficiencies. Numerical studies and a real data application show that these MLEs in RSS can be real competitors for those in SRS.</p>

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Some new results on parameter estimation of the exponential-Poisson distribution in ranked set sampling

  • 期刊论文

  • 发表日期：

    2025年6月26日

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  • Meng Chen,
  • Wang-xue Chen,
  • Cui-hong Deng

摘要

The existence and uniqueness of the maximum likelihood estimator (MLE) of parameter for the exponential-Poisson distribution is discussed by Kuş [2007. A new lifetime distribution. Computational Statistics and Data Analysis 51(9): 4497–4509] in simple random sampling (SRS). As an alternative to the MLEs in SRS, Joukar et al. [2021. Parameter estimation for the exponential-poisson distribution based on ranked set samples. Communication in Statistics-Theory and Methods 50(3): 560–581] discussed the MLE of parameter for this distribution in ranked set sampling (RSS). However, they did not discuss the existence and uniqueness of the MLE in RSS and did not provide explicit expressions for the Fisher information in RSS. In this article, we discuss the existence and uniqueness of the MLE of parameter in RSS and give explicit expressions for the Fisher information in RSS. The MLEs will be compared in terms of asymptotic efficiencies. Numerical studies and a real data application show that these MLEs in RSS can be real competitors for those in SRS.