**7. Conclusions**

A good theory should seek out the most concise explanation for the facts. With this in mind, a new modified form of BIII distribution has been introduced that can model well-specified forms of hazard rate shapes, including increasing, decreasing, bathtub, upside-down bathtub, and nearly constant. Some of its statistical properties, such as, *r*th moment, *s*th incomplete moment, moment generating function, skewness, kurtosis, mode, *i*th order statistics, and stochastic ordering have been derived. The maximum likelihood estimation is employed to estimate the model parameters. The usefulness of this model is demonstrated by applications on complete and censored samples. Simulation study is also performed. A future effort would include the contributions of new regression models, Bayesian parameter estimations, and research into diversified fields of data sets.

**Author Contributions:** F.J. gave the initial idea and proposed the new model. M.A.N. investigated mathematical properties. A.H.A. added the Middle-Censoring part of the paper. W.K.M. and M.H.T. wrote and structured the manuscript. S.K. investigated the numerical calculations applied to the data set and improved the overall presentation of the current draft. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study did not receive any funds in any aspects.

**Data Availability Statement:** The data used in the article are given therein.

**Acknowledgments:** The pre-print version of this paper is also freely available here https://hal. archives-ouvertes.fr/hal-01902854/document (accessed on 14 December 2021).

**Conflicts of Interest:** No conflict of interest was declared by the authors.
