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Characterizations of continuous distributions through inequalities involving the expected values of selected functions

Faranak Goodarzi;  Mohammad Amini;  Gholam Reza Mohtashami Borzadaran — 2017

Applications of Mathematics

Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser’s function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via w ( · ) -function defined by Cacoullos and Papathanasiou...

On lower bounds for the variance of functions of random variables

Faranak Goodarzi;  Mohammad Amini;  Gholam Reza Mohtashami Borzadaran — 2021

Applications of Mathematics

In this paper, we obtain lower bounds for the variance of a function of random variables in terms of measures of reliability and entropy. Also based on the obtained characterization via the lower bounds for the variance of a function of random variable X , we find a characterization of the weighted function corresponding to density function f ( x ) , in terms of Chernoff-type inequalities. Subsequently, we obtain monotonic relationships between variance residual life and dynamic cumulative residual entropy...

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