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Article
Correction to: Formulas of Absolute Moments
After publication of this paper, it was found out that there are still corrections which were not carried out in the proof. The publisher wish to apologize for this oversight.
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Article
Characterizations of the normal distribution via the independence of the sample mean and the feasible definite statistics with ordered arguments
It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov’s theorem, we further investigate the analogous characteristic propertie...
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Article
Formulas of Absolute Moments
The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat Hsu’s (J. Chinese Math. Soc. N.S. 1, 257–280, 1951) formulas ...
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Article
A Characterization of Exponential Distribution in Risk Model
In the general risk model (or the Sparre-Andersen model), it is well-known that the following assertion holds: if the claim size is exponentially distributed then the non-ruin probability distribution is a mix...
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Article
Characterizations of the exponential distribution by stochastic ordering properties of the geometric compound
Under the reliability NBU/NWU conditions, the exponential distribution is characterized by stochastic ordering properties which link the geometric compound with minimum order statistics or spacings of order st...
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Article
On a Characterization of the Gamma Distribution: The Independence of the Sample Mean and the Sample Coefficient of Variation
Let n≥ 3 and let X 1,...,X n be positive i.i.d. random variables whose common distribution function f has a continuous p.d.f. Using earlier work of the present authors and a me...
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Article
On the joint distribution of Grubbs' statistics
In this paper, the joint pdf's of Grubbs' statistics for normal and exponential populations are obtained; and relationship between the two pdf's is established. New formulations of the first marginal pdf of Gr...
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Article
On the joint distribution of studentized order statistics
In this paper, the joint distribution of some special linear combinations of the (internally) studentized order statistics are derived for both normal and exponential populations; the exact relationship betwee...
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Article
More comparisons of MLE with UMVUE for exponential families
Under some regularity conditions, the asymptotic expected deficiency (AED) of the maximum likelihood estimator (MLE) relative to the uniformly minimum variance unbiased estimator (UMVUE) for a given one-parame...
