On lower bounds for the variance of functions of random variables

Faranak Goodarzi; Mohammad Amini; Gholam Reza Mohtashami Borzadaran

Applications of Mathematics (2021)

  • Volume: 66, Issue: 5, page 767-788
  • ISSN: 0862-7940

Abstract

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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 and between variance past lifetime and dynamic cumulative past entropy. Moreover, we find lower bounds for the variance of functions of weighted random variables with specific weight functions applicable in reliability under suitable conditions.

How to cite

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Goodarzi, Faranak, Amini, Mohammad, and Mohtashami Borzadaran, Gholam Reza. "On lower bounds for the variance of functions of random variables." Applications of Mathematics 66.5 (2021): 767-788. <http://eudml.org/doc/298112>.

@article{Goodarzi2021,
abstract = {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 and between variance past lifetime and dynamic cumulative past entropy. Moreover, we find lower bounds for the variance of functions of weighted random variables with specific weight functions applicable in reliability under suitable conditions.},
author = {Goodarzi, Faranak, Amini, Mohammad, Mohtashami Borzadaran, Gholam Reza},
journal = {Applications of Mathematics},
keywords = {variance bound; Chernoff inequality; size-biased distribution; reliability measure; dynamic cumulative residual entropy; dynamic cumulative past entropy},
language = {eng},
number = {5},
pages = {767-788},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On lower bounds for the variance of functions of random variables},
url = {http://eudml.org/doc/298112},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Goodarzi, Faranak
AU - Amini, Mohammad
AU - Mohtashami Borzadaran, Gholam Reza
TI - On lower bounds for the variance of functions of random variables
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 5
SP - 767
EP - 788
AB - 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 and between variance past lifetime and dynamic cumulative past entropy. Moreover, we find lower bounds for the variance of functions of weighted random variables with specific weight functions applicable in reliability under suitable conditions.
LA - eng
KW - variance bound; Chernoff inequality; size-biased distribution; reliability measure; dynamic cumulative residual entropy; dynamic cumulative past entropy
UR - http://eudml.org/doc/298112
ER -

References

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