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The asymptotic normality of an intermediate order statistic of the ranges of sub-samples

โœ Scribed by J. W. H. Swanepoel

Publisher
Springer Japan
Year
1993
Tongue
English
Weight
378 KB
Volume
45
Category
Article
ISSN
0020-3157

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Let X1; X2; : : : be independent observations from the absolutely continuous distribution function F with quantile function Q. The density of the normalized order statistic X n-kn+1 : n converges locally uniformly to the standard normal density for any sequence kn with kn โ†’ โˆž and kn=n โ†’ 0 if and onl

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Let X1; X2; : : : ; Xn be a sequence of independent, identically distributed positive integer random variables. We study the asymptotics of the likelihood that the sample maximum is achieved k times and in its spacing relative to the second highest value. Earlier and other results are discussed in c