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<p>In this paper we estimate the parameters of generalized Rayleigh distribution when data obtained using variations of ranked set sampling techniques: moving extreme ranked set sampling (MERSS), quartile ranked set sampling (QRSS), extreme ranked set sampling (ERSS), and median ranked set sampling (MRSS) as an alternatives to simple random sampling (SRS). We develop maximum likelihood functions and derive the corresponding likelihood equations. We construct expressions for Fisher’s information matrix under ERSS, MRSS, QRSS, and MERSS. Through simulation, we compute maximum likelihood estimates, mean square error, bias of estimates, and observed Fisher information. The simulation results indicate that the MERSS method yields estimates with lower biases and mean square errors compared to the ERSS, MRSS, and QRSS methods. The real data set is used to show the performance of the MERSS scheme.</p>

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Parameter Estimation of Generalized Rayleigh Distribution

  • 期刊论文

  • 发表日期：

    2025年3月28日

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  • Vyomesh Nandurbarkar

摘要

In this paper we estimate the parameters of generalized Rayleigh distribution when data obtained using variations of ranked set sampling techniques: moving extreme ranked set sampling (MERSS), quartile ranked set sampling (QRSS), extreme ranked set sampling (ERSS), and median ranked set sampling (MRSS) as an alternatives to simple random sampling (SRS). We develop maximum likelihood functions and derive the corresponding likelihood equations. We construct expressions for Fisher’s information matrix under ERSS, MRSS, QRSS, and MERSS. Through simulation, we compute maximum likelihood estimates, mean square error, bias of estimates, and observed Fisher information. The simulation results indicate that the MERSS method yields estimates with lower biases and mean square errors compared to the ERSS, MRSS, and QRSS methods. The real data set is used to show the performance of the MERSS scheme.