Geodesic
Note on Dispersion of Xalpha
Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 23

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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/
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     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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