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

Faranak Goodarzi; Mohammad Amini; Gholam Reza Mohtashami Borzadaran

Applications of Mathematics (2017)

  • Volume: 62, Issue: 5, page 493-507
  • ISSN: 0862-7940

Abstract

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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 ( · ) -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.

How to cite

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Goodarzi, Faranak, Amini, Mohammad, and Mohtashami Borzadaran, Gholam Reza. "Characterizations of continuous distributions through inequalities involving the expected values of selected functions." Applications of Mathematics 62.5 (2017): 493-507. <http://eudml.org/doc/294520>.

@article{Goodarzi2017,
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 $w(\cdot )$-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.},
author = {Goodarzi, Faranak, Amini, Mohammad, Mohtashami Borzadaran, Gholam Reza},
journal = {Applications of Mathematics},
keywords = {characterization; hazard rate; mean residual life function; reversed hazard rate; expected inactivity time; log-odds rate; Glaser's function},
language = {eng},
number = {5},
pages = {493-507},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizations of continuous distributions through inequalities involving the expected values of selected functions},
url = {http://eudml.org/doc/294520},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Goodarzi, Faranak
AU - Amini, Mohammad
AU - Mohtashami Borzadaran, Gholam Reza
TI - Characterizations of continuous distributions through inequalities involving the expected values of selected functions
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 5
SP - 493
EP - 507
AB - 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.
LA - eng
KW - characterization; hazard rate; mean residual life function; reversed hazard rate; expected inactivity time; log-odds rate; Glaser's function
UR - http://eudml.org/doc/294520
ER -

References

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