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On lower bounds for the variance of functions of random variables

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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.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions that improved the quality of the paper.

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Authors and Affiliations

  1. Department of Statistics, University of Kashan, 8731753153, Kashan, Iran

    Faranak Goodarzi

  2. Department of Statistics, Ordered Data, Reliability and Dependency Center of Excellence, Ferdowsi University of Mashhad, P.O.Box 91775-1159, Mashhad, Iran

    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.

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Goodarzi, F., Amini, M. & Mohtashami Borzadaran, G.R. On lower bounds for the variance of functions of random variables. Appl Math 66, 767–788 (2021). https://doi.org/10.21136/AM.2021.0042-20

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  • DOI: https://doi.org/10.21136/AM.2021.0042-20

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