Abstract
In this note we prove some inequalities for variances and other measures of deviation of functions of random variables. Based on these inequalities we find some corollaries concerning the variances of fractional powers of random variables and of sums of independent random variables.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beesack, P. R.: Inequalities for absolute moments of a distribution: From Laplace to von Mises. J. Math. Anal. Appl. 98 (1984), 435–457
Petrov, W. W.: Limit Theorems for sums of independent random variables. (russ.) Nauka, Moscow (1987)
Wolfe, S. J.: On moments of probability distribution functions. in: Lect. Notes in Math., Vol. 457 (Fractional calculus and applications, ed. by B. Ross) 306–316 Springer-Verlag, Berlin-Heidelberg (1975)
Banjević, D. and Bratičević, D.: Note on dispersion ofX α. Publications of the department of Mathematics (University of Belgrade), 33 (47), 1983, 23–28
Krickeberg, K. und Ziezold, H.: Stochastische Methoden, 3. Aufl., Springer-Verlag, Berlin-Heidelberg (1988)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nollau, V. Inequalities for variances of some functions of random variables. Stat Papers 36, 163–174 (1995). https://doi.org/10.1007/BF02926029
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02926029