On the compatibility of Dyson's conditions

Kenneth S. Berenhaut, Donghui Chen and Vy Tran

Statistics & Probability Letters, 2008, vol. 78, issue 17, 3110-3113

Abstract: This short note adds to the existing knowledge on interpretation of the concept of kurtosis with regard to density crossing points. Local limit theorems are employed to show that, in the skew case, the conditions of a well-known theorem of Dyson cannot hold concurrently for standardized sums of independent and identically distributed random variables, for sufficiently large samples. A binomial example is considered.

Date: 2008
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