We exhibit a general family of distributions named “Kumaraswamy odd Burr G family of distributions” with four additional parameters to generalize any existing baseline distribution. Some statistical properties of the family are derived, including rth moments, mth incomplete moments, moment generating function and entropies. The parameters of the family are estimated by the maximum likelihood (ML) method for complete sam- ples as well as censored samples. Some sub-models of the family are considered and it is noted that their density functions can be symmetric, left-skewed, right-skewed, unimodal, bimodal and their hazard rate functions can be increasing, decreasing, bathtub, upside- down bathtub and J-shaped. Simulation is carried out for one of the sub-models to check the asymptotic behavior of the ML estimates. Applications to reliability (complete and censored) data are carried out to check the usefulness of some sub-models of the family.
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