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In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see the performance of maximum likelihood estimates (MLEs) of the MBXII-Power distribution. The potentiality of the MBXII-Power distribution is demonstrated by its application to real data sets: survival times of pigs, survival times of patients and quarterly earnings
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