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Oluyede et al. (2016) and Mdlongwa et al. (2017) consider the continuous univariate distributions called Dagum-Poisson (DP) and Burr XII Modified Weibull (BXIIMW), respectively, and study certain properties and applications of these distributions. Shahid and Raheel (2019) and Para and Jan (2019) proposed the univariate discrete distributions called Discrete Modified Inverse Rayleigh (DMIR) and Discrete Generalized Inverse Weibull (DGIW) and study some of their mathematical properties. The present short note is intended to complete, in some way, the works cited above via establishing certain characterizations of these distributions in different directions.

On Characterizations of Four Recently Introduced Distributions: Two Continuous and Two Discrete