Geodesic
Note on Dispersion of Xalpha
Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 23 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Some inequalities for moments of $X^\alpha$, $0\alpha\leq 1$, $X$ nonneg. r. v., are presented, for example $DX^\alpha\leq (DX)^\alpha$, $DX^\alpha\leq (DX)/(EX)^{2(1-\alpha)}$, $ (EX)^\alpha-EX^\alpha \leq (1-\alpha)(DX)/(EX)^{2-\alpha}. $ It is proved that $nD\overline X_n^\alpha\to\alpha^2(DX)/(EX)^{2(1-\alpha)}$, $n\to\infty$, where $X_1,X_2,\dots,X_n$ are i. \i d. r. v. and $\overline X_n= (X_1+X_2+\dots+ X_n)/n$. The estimation of $\sqrt{EX}$ is considered, and for binominal case some numerical evaluations are given.
Classification : 60E15 62F10 62F11 62F12
Keywords: nonnegative random variables, inequalities for moments, unbias estimation, binomial distribution 
@article{PIM_1983_N_S_33_47_a2,
     author = {Dragan Banjevi\'c and D. Brati\v{c}evi\'c},
     title = {Note on {Dispersion} of {Xalpha}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {23 },
     year = {1983},
     volume = {_N_S_33},
     number = {47},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a2/}
}
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Dragan Banjević; D. Bratičević. Note on Dispersion of Xalpha. Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 23 . http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a2/