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In this paper, a flexible lifetime distribution with increasing, decreasing, increasing-decreasing-increasing and bathtub hazard function, called New Family of Kies Burr III (NFKBIII) distributions is proposed. The density function of the NFKBIII is arc, J, reverse-J, U, bimodal, left-skewed, right-skewed and symmetrical shaped. The NFKBIII distribution is developed on the basis of the T-X family technique. The NFKBIII distribution is also obtained from compounding mixture distributions. Some structural and mathematical properties including moments, inequality measures, order statistics and reliability measures are theoretically established. The NFKBIII distribution is characterized via different techniques. Parameters of the NFKBIII distribution are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of the NFKBIII distribution is demonstrated via its application to real data sets.

ON NEW FAMILY OF KIES BURR III DISTRIBUTION: Development, Properties, Characterizations, and Application