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Keywords:
total time on test transform; generalized failure rate; generalized reversed failure rate; new better than used in total time on test transform; weight function
total time on test transform; generalized failure rate; generalized reversed failure rate; new better than used in total time on test transform; weight function
Summary:
Although the total time on test (\textit{TTT}) transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the \textit{TTT} transform for the weighted random variables and investigates the behavior of the failure rate function of such variables based on the \textit{TTT} transform. In addition, the conditions for establishing the $TTT$ transform ordering for weight variables and its relationship with some stochastic orders have been investigated, and the conditions for establishing the \textit{TTT} transform order as well as the presentation of the new better than used in total time on test transform (\textit{NBUT}) class of the weighted variables have also been studied. Finally, by analyzing the real data sets, applications of the transform introduced in the fit of a model is presented, and it is shown that weighted models have a significant advantage over the base models.
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