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A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications

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  • Alya Al Mutairi
  • Muhammad Z. Arshad

Abstract

Modeling complex random phenomena frequently observed in reliability engineering and medical science once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. We contribute a new family referred to as an odd Fréchet Lehmann type-II (OFrLII) G family of distributions to address these issues. This new family has involved a shape parameter that modulated the tails of new models. Furthermore, we develop a list of eight new sub-models for a new family and a power function distribution (OFrLII–PF) nominated for detailed discussion. We derive several complementary mathematical properties and explicit expressions for the moments, quantile function, and order statistics. We plot possible shapes of the density and the hazard rate functions over the particular choices of the model parameters. We follow a technique known as maximum likelihood estimation to estimate unknown model parameters and a simulation study established to assess the asymptotic behavior of these MLEs. The applicability of the OFrLII–G family, is evaluated via OFrLII –PF distribution. For this, we fit two engineering and one COVID–19 pandemic dataset. Supportive results of OFrLII–PF distribution declare it as a better fit model against the well-established competitor’s ones. A modified odd Fréchet Lehmann Type II–G Family of Distributions- A Power Function Distribution with Theory and Applications

Suggested Citation

  • Alya Al Mutairi & Muhammad Z. Arshad, 2022. "A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(2), pages 1-29, March.
    • Handle: RePEc:ibn:ijspjl:v:11:y:2022:i:2:p:29
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    References listed on IDEAS

    as
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    3. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    4. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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