On characterization of some distributions by variance bounds

Cacoullos and Papathanasiou (1989) obtained a characterization for the distribution of a random variable via w(.)-functions and the lower bounds for the variance of a given function of that random variable. In this paper, on the basis of their work, we derive a characterization for the inverse gamma distribution, the exp-uniform distribution and the exponentiated exponential distribution. Moreover, in terms of generalization of Chernoff-type inequalities by Afendras et al. (2011), we find the lower bound for the variance of a function of the inverse gamma random variable.