On the Kavya–Manoharan–Burr X Model: Estimations under Ranked Set Sampling and Applications

Osama H. Mahmoud Hassan (), Ibrahim Elbatal, Abdullah H. Al-Nefaie and Mohammed Elgarhy
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Osama H. Mahmoud Hassan: Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Ibrahim Elbatal: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
Abdullah H. Al-Nefaie: Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Mohammed Elgarhy: The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt

JRFM, 2022, vol. 16, issue 1, 1-20

Abstract: A new two-parameter model is proposed using the Kavya–Manoharan (KM) transformation family and Burr X (B X ) distribution. The new model is called the Kavya–Manoharan–Burr X (KMB X ) model. The statistical properties are obtained, involving the quantile (Q U ) function, moment (M O s), incomplete M O s, conditional M O s, M O -generating function, and entropy. Based on simple random sampling (S i R S ) and ranked set sampling (R a S S ), the model parameters are estimated via the maximum likelihood (ML L ) method. A simulation experiment is used to compare these estimators based on the bias (B I ), mean square error (M S E R ), and efficiency. The estimates conducted using R a S S tend to be more efficient than the estimates based on S i R S . The importance and applicability of the KMB X model are demonstrated using three different data sets. Some of the useful actuarial risk measures, such as the value at risk and conditional value at risk, are discussed.

Keywords: KM transformation family; Burr X distribution; moments; entropy; approach of maximum likelihood (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2022
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