Abstract
We introduce a new extension of the reciprocal Exponential distribution for modeling the extreme values. We used the Morgenstern family and the clayton copula for deriving many bivariate and multivariate extensions of the new model. Some of its properties are derived. We assessed the performance of the maximum likelihood estimators (MLEs) via a graphical simulation study. The assessment was based on the sample size. The new reciprocal model is employed for modeling the skewed and the symmetric real data sets. The new reciprocal model is better than some other important competitive models in statistical modeling.
Highlights
A Generalization of Reciprocal Exponential ModelMansour[1,2], Nadeem Shafique Butt3*, Haitham M
A random variable (RV) Y is said to have the reciprocal Exponential (RE) distribution if its probability density function (P-D-F) and cumulative distribution function (C-D-F) are given by gc3(y) = c3y−2e−cy3|y≥0 (1) andGc3(y) = e−cy3|y≥0, (2)where c3 > 0 is a scale parameter
The bivariate extension via clayton copula can be considered as a weighted version of the clayton copula, which is of the form
Summary
For c1 = 1 we get the Proportional reversed hazard rate G family Gupta and Gupta (2007). We define a new RE model based on Cordeiro (2017)] called generalized odd log-logistic RE (GOLL-RE) family and provide some plots of its P-D-F and hazard rate function (H-R-F). Some plots of the GOLL-RE P-D-F and H-R-F are given in Figure 1 (see Appendix A for all Tables and Appendix B for all Figures) to illustrate some of its characteristics. For simulation of this new model, we obtain the quantile function (QF) of y (by inverting (5)), say yu = Q(u) = F−1(u), as. (2018), Korkmaz et al, (2018), Yousof et al, (2018 b), Hamedani et al, (2019), Goual and Yousof (2019) and Korkmaz et al, (2019), among others
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