On upper bounds for the variance of functions of random variables with weighted distributions
- Authors: Goodarzi F.1, Amini M.1, Mohtashami Borzadaran G.R.1
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Affiliations:
- Department of Statistics
- Issue: Vol 37, No 4 (2016)
- Pages: 422-435
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198033
- DOI: https://doi.org/10.1134/S1995080216040089
- ID: 198033
Cite item
Abstract
Cacoullos and Papathanasiou (1989) obtained a characterization for the distribution of a random variable via the upper bounds for the variance of a given function of that random variable. In this paper, on the basis of their works, we derive a characterization for the weighted distribution. Subsequently, by using the characterization and in terms of Chernoff-type inequalities, we find the upper bounds for the variance of a given function of the weighted random variable. Moreover, assuming that X is IFR [increasing failure rate] we compute an upper bound for the variance of this function.
About the authors
F. Goodarzi
Department of Statistics
Author for correspondence.
Email: goodarzi_kh@yahoo.com
Iran, Islamic Republic of, Mashhad, 91775
M. Amini
Department of Statistics
Email: goodarzi_kh@yahoo.com
Iran, Islamic Republic of, Mashhad, 91775
G. R. Mohtashami Borzadaran
Department of Statistics
Email: goodarzi_kh@yahoo.com
Iran, Islamic Republic of, Mashhad, 91775