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In this paper, a flexible distribution with increasing, bathtub and inverted bathtub hazard rate called Modified Burr III-Power (MBIII-Power) is developed on the basis of the generalized Pearson differential equation. The density function of MBIII-Power is arc, exponential and positively skewed shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBIII-Power distribution is characterized via different techniques. Parameters of MBIII-Power distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). Potential use of MBIII-Power distribution is demonstrated by its application to two data sets: serum-reversal time (in days) of children born from HIV-infected mothers and failure times of device data.

On modified Burr III-power distribution: Development, properties, characterizations, and applications