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Type-I heavy tailed family with applications in medicine, engineering and insurance

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  • Wei Zhao
  • Saima K Khosa
  • Zubair Ahmad
  • Muhammad Aslam
  • Ahmed Z Afify

Abstract

In the present study, a new class of heavy tailed distributions using the T-X family approach is introduced. The proposed family is called type-I heavy tailed family. A special model of the proposed class, named Type-I Heavy Tailed Weibull (TI-HTW) model is studied in detail. We adopt the approach of maximum likelihood estimation for estimating its parameters, and assess the maximum likelihood performance based on biases and mean squared errors via a Monte Carlo simulation framework. Actuarial quantities such as value at risk and tail value at risk are derived. A simulation study for these actuarial measures is conducted, proving that the proposed TI-HTW is a heavy-tailed model. Finally, we provide a comparative study to illustrate the proposed method by analyzing three real data sets from different disciplines such as reliability engineering, bio-medical and financial sciences. The analytical results of the new TI-HTW model are compared with the Weibull and some other non-nested distributions. The Baysesian analysis is discussed to measure the model complexity based on the deviance information criterion.

Suggested Citation

  • Wei Zhao & Saima K Khosa & Zubair Ahmad & Muhammad Aslam & Ahmed Z Afify, 2020. "Type-I heavy tailed family with applications in medicine, engineering and insurance," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.
    • Handle: RePEc:plo:pone00:0237462
    DOI: 10.1371/journal.pone.0237462
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    References listed on IDEAS

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    Cited by:

    1. Nada M. Alfaer & Ahmed M. Gemeay & Hassan M. Aljohani & Ahmed Z. Afify, 2021. "The Extended Log-Logistic Distribution: Inference and Actuarial Applications," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    2. Wanting Wang & Zubair Ahmad & Omid Kharazmi & Clement Boateng Ampadu & E H Hafez & Marwa M Mohie El-Din, 2021. "New generalized-X family: Modeling the reliability engineering applications," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-26, March.

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