Abstract
In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.
Highlights
Several generalized families of univariate distribution have been constructed based on classical distributions
We introduce two special models of the transmuted Burr X-G (TBX-G) family based on the exponential and log-logistic models to generate the TBXE and TBXLL distributions, which can provide unimodal, symmetrical, left-skewed, right-skewed, and reversed-Jshaped densities; and decreasing, increasing, bathtub, upside-down bathtub, J-shaped, and reversed-J shaped hazard rates (Figures 1 and 2)
Some mathematical properties of the TBX-G family can be confirmed through an algebraic expansion in terms of exponential-G (Exp-G) distribution, which is more efficient than directly computing those by numerical integration of its probability density function (PDF)
Summary
Several generalized families ( known as generators) of univariate distribution have been constructed based on classical distributions These generators provide greater flexibility by adding one or more parameters to a baseline model. The TBX-G is a wider family of continuous distributions It includes the BX-G family and provides greater flexibility in modeling real life data. We summarize the findings of the proposed TBX-G class as follows: (1) Its sub-models provide unimodal, symmetrical, left-skewed, right-skewed, and reversed-J densities. They have decreasing, increasing, bathtub, upside-down bathtub, J-shaped, and reversed-J shaped hazard rates, which are frequently encountered in real-life applied areas.
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