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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Osama H. Mahmoud Hassan & Ibrahim Elbatal & Abdullah H. Al-Nefaie & Mohammed Elgarhy, 2022. "On the Kavya–Manoharan–Burr X Model: Estimations under Ranked Set Sampling and Applications," JRFM, MDPI, vol. 16(1), pages 1-20, December.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2022:i:1:p:19-:d:1017598
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    References listed on IDEAS

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    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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