Abstract
The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.
Highlights
We refer to the papers of [10] for the Marshall–Olkin class, [11] for the Beta and Gamma classes, [12] for the odd exponentiated half-logistic-G (OEHL-G) family, [13] for the flexible Weibull class, [14] for the odd log-logistic Lindley class, [15] for the odd Chen class, [16] for the exponentiated odd Chen class, [17] for a new Kumaraswamy generalized class, [18,19] for the extended
The probability density function (PDF) of the odd exponentiated half-logistic inverse exponential (OEHLIEx) model can be represented as an infinite mixture of an exponentiated inverse exponential (IEx) (Exp-IEx) distribution:
We derive the Maximum Likelihood Estimation (MLE) of the unknown parameters λ, β, and α of the OEHLIEx model based on complete samples
Summary
Many generalized classes of life time distributions have been discussed in the literature It has been proven in many papers that the new generalizations are more flexible in modelling and better fit real-life data. These new distributions have several desirable properties such as the asymptotic behavior of their probability density function and the hazard rate function’s monotonicity, which has made them superior to the original distribution. All of this has encouraged authors to work more on developing new lifetime distributions using different generalization methods. It can be used to model over- and under-dispersed data (See Section 6)
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