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

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Abstract

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 (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.

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Authors and Affiliations

  1. Department of Statistics, Ordered and Spatial Data Center of Excellence Faculty of Mathematical Sciences Ferdowsi University of Mashhad, Mashhad, Iran

    Faranak Goodarzi, Mohammad Amini & Gholam Reza Mohtashami Borzadaran

Authors
  1. Faranak Goodarzi
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  2. Mohammad Amini
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  3. Gholam Reza Mohtashami Borzadaran
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Correspondence to Faranak Goodarzi.

Additional information

This research has been supported by a grant from Ferdowsi University of Mashhad (No. 2/43905).

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Goodarzi, F., Amini, M. & Mohtashami Borzadaran, G.R. Characterizations of continuous distributions through inequalities involving the expected values of selected functions. Appl Math 62, 493–507 (2017). https://doi.org/10.21136/AM.2017.0182-16

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