Parameter Estimation of Generalized Rayleigh Distribution

• Published in: Journal of statistical theory and practice Vol. 19; no. 2
• Main Author: Nandurbarkar, Vyomesh
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2025
• Subjects: Mathematics and Statistics; Original Article; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics; Maximum likelihood estimator; 62F07; Observed Fisher information; Extreme ranked set sampling; 62F10; Moving extreme ranked set sampling; 62D05
• ISSN: 1559-8608; 1559-8616
• DOI: 10.1007/s42519-025-00437-3

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.