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- W1947128113 abstract "In this paper, earlier works of the present authors and a method due to Anosov for solving certain intego-functional equations are combined to show that the independence of the sample mean $bar{X}_n$ and the $Z_n$-statistic characterizes the normal population, when the random samples are iid from a population having a continuous density function on ${Bbb R}$, and the sample size $ngeq 3$; obviously the sample standard deviation is a $Z_n$-statistic. Further, an important subclass of $Z_n$-statistic with the form of a linear combination $sum^n_{i=1} a_iX_{(i)}$ of order statistics is found, where $a_1 leq cdots leq a_n$, not all equal and $sum^n_{i=1}a_i=0$, which includes Gini$^prime$s mean difference and the sample range but not the sample standard deviation. Similar approach can be applied to prove that the independence of $bar{X}_n$ and $Z_n/bar{X}_n$ characterizes the gamma distribution; obviously the independence of sample mean and sample coefficient of variation characterizes the gamma distribution. The study of identifying $Z_n$ to more known statistics will be the future work." @default.
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- W1947128113 date "2000-01-09" @default.
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- W1947128113 title "ON SOME CHARACTERIZATIONS OF POPULATION DISTRIBUTIONS" @default.
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- W1947128113 doi "https://doi.org/10.11650/tjm.4.2000.1287" @default.
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