Geodesic
Characterizations of continuous distributions through inequalities involving the expected values of selected functions
Applications of Mathematics, Tome 62 (2017) no. 5, pp. 493-507.

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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 $w(\cdot )$-function defined by Cacoullos and Papathanasiou (1989), characterize exponential and logistic distributions, as well as Type 3 extreme value distribution and obtain bounds for the expected values of selected functions in reliability theory. Moreover, a bound for the varentropy of random variable $X$ is provided.
DOI : 10.21136/AM.2017.0182-16
Classification : 60E15, 62E10
Keywords: characterization; hazard rate; mean residual life function; reversed hazard rate; expected inactivity time; log-odds rate; Glaser's function 
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Goodarzi, Faranak; Amini, Mohammad; Mohtashami Borzadaran, Gholam Reza. Characterizations of continuous distributions through inequalities involving the expected values of selected functions. Applications of Mathematics, Tome 62 (2017) no. 5, pp. 493-507. doi : 10.21136/AM.2017.0182-16. http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0182-16/

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