Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling

S. P. Arun; M. R. Irshad; R. Maya; Amer I. Al-Omari; Shokrya S. Alshqaq; S. P. Arun; M. R. Irshad; R. Maya; Amer I. Al-Omari; Shokrya S. Alshqaq

doi:10.3934/math.2025098

AIMS Mathematics

2025, Volume 10, Issue 2: 2083-2097. doi: 10.3934/math.2025098

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Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling

S. P. Arun ^{1
,
,},
M. R. Irshad ^{2
,},
R. Maya ^{2
,},
Amer I. Al-Omari ^{3
,
,},
Shokrya S. Alshqaq ^{4
,}

1.
Kerala University Library, Research Centre, University of Kerala, Thiruvananthapuram 695034, India
2.
Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India; irshadmr@cusat.ac.in, publicationsofmaya@gmail.com
3.
Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 251113, Jordan
4.
College of Science, Jazan University, P.O.Box. 114, Jazan 45142, Kingdom of Saudi Arabia; salshekak@jazanu.edu.sa

Received: 17 October 2024 Revised: 03 January 2025 Accepted: 17 January 2025 Published: 08 February 2025
MSC : 62G30, 62F10

Ranked set sampling is a well-known and efficient method compared to simple random sampling for estimating population parameters. In this study, we focus on the challenge of estimating the scale parameter of the primary variable $Z$ using a multistage ranked set sample obtained by ordering the marginal observations of an auxiliary variable $W$ , where the pair $(W, Z)$ follows the Farlie–Gumbel–Morgenstern bivariate Bilal distribution. Assuming that the dependence parameter $\phi$ is known, we introduce the best linear unbiased estimator for the scale parameter of the primary variable, utilizing a multistage ranked set sample. We also compare the efficiency of the proposed estimator with that of the maximum likelihood estimator based on the same number of measured units. It is found that the suggested estimators are more efficient than the classical estimators considered in this study.

Keywords:

Citation: S. P. Arun, M. R. Irshad, R. Maya, Amer I. Al-Omari, Shokrya S. Alshqaq. Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling[J]. AIMS Mathematics, 2025, 10(2): 2083-2097. doi: 10.3934/math.2025098

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Abstract

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