A Measure of Variability Based on the Harmonic Mean, and Its Use in Approximations
Brown, Mark
Ann. Statist., Tome 13 (1985) no. 1, p. 1239-1243 / Harvested from Project Euclid
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Let $X$ be a positive random variable and assume that both $a = EX^{-1}$ and $\mu = EX$ are finite. Define $c^2 = 1 - (a\mu)^{-1}$. This quantity serves as a measure of variability for $X$ which is reflected in the behavior of completely monotone functions of $X$. For $g$ completely monotone with $g(0) < \infty$: $0 \leq Eg(X) - g(EX) \leq c^2g(0) \text{and}\operatorname{Var} g(X) \leq c^2g^2(0).$
Publié le : 1985-09-14
Classification:  Completely monotone functions,  variability,  harmonic mean,  Laplace transforms,  NWUE distributions,  60E15,  62N99 
@article{1176349668,
     author = {Brown, Mark},
     title = {A Measure of Variability Based on the Harmonic Mean, and Its Use in Approximations},
     journal = {Ann. Statist.},
     volume = {13},
     number = {1},
     year = {1985},
     pages = { 1239-1243},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176349668}
}

Brown, Mark. A Measure of Variability Based on the Harmonic Mean, and Its Use in Approximations. Ann. Statist., Tome 13 (1985) no. 1, pp.  1239-1243. http://gdmltest.u-ga.fr/item/1176349668/