Parameter estimation of exponentiated exponential distribution under selective ranked set sampling

Amal S. Hassan; Rasha S. Elshaarawy; Heba F. Nagy

doi:10.2478/stattrans-2022-0041

Parameter estimation of exponentiated exponential distribution under selective ranked set sampling

Amal S. Hassan Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt ORCID:https://orcid.org/0000-0003-4442-8458 , Rasha S. Elshaarawy Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt ORCID:https://orcid.org/0000-0001-7414-3950 , Heba F. Nagy Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt ORCID:https://orcid.org/0000-0003-0262-205X Statistics in Transition new series, vol. 23, 2022, 4, pages: 37-58 Published online: 15 December 2022 DOI 10.2478/stattrans-2022-0041

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ABSTRACT

Partial ranked set sampling (PRSS) is a cost-effective sampling method. It is a combination of simple random sample (SRS) and ranked set sampling (RSS) designs. The PRSS method allows flexibility for the experimenter in selecting the sample when it is either difficult to rank the units within each set with full confidence or when experimental units are not available. In this article, we introduce and define the likelihood function of any probability distribution under the PRSS scheme. The performance of the maximum likelihood estimators is examined when the available data are assumed to have an exponentiated exponential (EE) distribution via some selective RSS schemes as well as SRS. The suggested ranked schemes include the PRSS, RSS, neoteric RSS (NRSS), and extreme RSS (ERSS). An intensive simulation study was conducted to compare and explore the behaviour of the proposed estimators. The study demonstrated that the maximum likelihood estimators via PRSS, NRSS, ERSS, and RSS schemes are more efficient than the corresponding estimators under SRS. A real data set is presented for illustrative purposes.

KEYWORDS

exponentiated exponential distribution, partial ranked set sampling, neoteric ranked set sampling, maximum likelihood method

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