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In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.

On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations and Applications