The exact and approximate distributions of linear combinations of selected order statistics from a uniform distribution |
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Authors: | T Matsunawa |
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Abstract: | Summary The exact probability density function is given for linear combinations ofk=k(n) order statistics selected from whole order statistics based on random sample of sizen drawn from a uniform distribution. Normal approximation to the linear combinations is made with the aid of Berry-Esseen's
theorem. Necessary and sufficient conditions of the asymptotic normality for the statistic are obtained, too. An exact distribution
and its normal approximation of linear combination of mutually independent gamma variables with integer valued parameters
are also given as associated consequences.
The Institute of Statistical Mathematics |
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Keywords: | Linear combination order statistics uniform distribution exact distribution normal approximation |
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