SAMPLE-LIKE DISTRIBUTION OF AN ORDER STATISTIC UNDER GENERAL NONSAMPLE CONDITIONS AND SOME ASYMPTOTIC IMPLICATIONS,
Abstract
Consider n univariate observations having an arbitrary joint distribution. In general, the distribution of any order statistic of these observations is shown to be the same as that of this order statistic for a random sample of size n (from a distribution determined by the joint distribution). Thus, individual order statistics can be considered to arise from samples. However, the distribution 'sampled' can change greatly with the order statistic. These results are useful in determining asymptotic distributional properties of extremes and percentage points of the observations. That is, for given large n, an asymptotic distribution developed assuming a sample is usable for the more general situation if the distribution 'sampled' has a suitable form. Thus, for the continuous case, observed percentage points have asymptotically normal distributions under very general conditions. Also, asymptotic distributions developed for extremes of samples should often be usable for continuous situations. Applications of these asymptotic results for prediction are discussed for situations where several sets of observations (same n for each set) are independently obtained from approximately the same source. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 07, 1968
- Accession Number
- AD0680440
Entities
People
- John E. Walsh
Organizations
- Southern Methodist University