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
Highlights
Over a long time, modeling complex random phenomena predominantly in reliability engineering and medical sciences consider an enigma for researchers
We develop a list of eight new sub-models for a new family and a power function distribution (OFrLII–PF) nominated for detailed discussion
An odd Fréchet Lehmann type-II (OFrLII) G family random variable X corresponding to fOFrLII−G(x; φ) will be denoted by X~ OFrLII –G(x; φ) and to the best of our knowledge, no study has been done in the past that relates to our new family
Summary
Over a long time, modeling complex random phenomena predominantly in reliability engineering and medical sciences consider an enigma for researchers. In the meantime, [3] proposed a new technique to generate models with CDF [P(z)⁄(P(z) + aP(z))]. Study by [4] proposed a beta generated–P family with CDF F(x) = ∫0Z(x) b(t) dt, where b(t) is the PDF of beta distribution with G(x; ζ) ε (0,1) is a CDF of any arbitrary baseline model. [9] developed a dual transformation and established a Lehmann type–II (L–II) P family with CDF Z(x) = 1 − (1 − P(z))a. [13] proposed a DUS transformation to generate new models with CDF [(eP(z). [17] proposed a new alpha power transformation with CDF [P(z)αP(z)⁄α]. Study by [18] proposed another technique with CDF [(aP(z) − eP(z))⁄(a − e)] to generate new models. See the latest work of the references. [22] generalized a new model via L–II–P family. [23] discussed exponentiated PF distribution with L–I. [24] developed a generalized version of L–II. [25] developed the P family of a generalized version of L–II with CDF [1 − ((1 − P(z))⁄(1 − aP(z)))b], and [26] discussed a beta version of L–II with CDF [I1−(1−P(z))a(a, b)]
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