Abstract:

A new distribution with flexible hazard rate function is introduced which is called new modified Burr XII (NMBXII) distribution. The proposed distribution is derived from the T-X family technique and compounding the generalized Nadarajah–Haghighi (GNH) and gamma distributions. We highlighted the shapes of NMBXII density and failure rate functions. The density function of NMBXII model can take shapes such as J, reverse J, positively skewed and symmetrical.  The proposed model can produce almost all types of failure rates such as increasing, decreasing, increasing-decreasing, decreasing-increasing, bimodal, inverted bathtub and modified bathtub. To show the importance of the proposed distribution, we established various mathematical properties such as quantiles, moments, incomplete moments, inequality measures, residual life functions and reliability measures theoretically.  We have characterized the NMBXII distribution via two techniques. We addressed the maximum likelihood estimation technique for model parameters. The precision of the MLEs is estimated via a simulation study. We have considered three real data sets for applications to demonstrate the potentiality and utility of the NMBXII model. Then, we have established empirically that the proposed model is suitable for tax revenue, time periods between successive earthquakes and flood discharges applications. Finally, various model selection criteria, the goodness of fit statistics and graphical tools were used to examine the adequacy of the NMBXII distribution. 

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