ON MOMENTS OF ORDER STATISTICS AND QUASI-RANGES FROM NORMAL POPULATIONS
Abstract
Various results on order statistics (OS) of a sample from the standard normal population are unified, and these results are supplemented with new results. Simple recursion formulae among the first, second and mixed (linear) moments are derived. There is a discussion about the lower bound on the number of integrals to be evaluated in order to know the first, second and mixed (linear) moments of all OS for any sample size N, assuming that these moments are available for the preceding N, namely (N-1). It is shown that it is sufficient to evaluate at most (N-2)/2 integrals when N is even and (N-1)/2 integrals when N is odd. The recursion formulae can be used to work downwards in numerical evaluation of the moments of order statistics, without serious accumulation of rounding errors. Using the relationship between the sample quasi-ranges and order statistics in the sample, the expected values, variances and covariances of sample quasi-ranges from the normal population were expressed in terms of expected values, variances and covariances of order statistics in the sample. Simple recursion formulae among the expected values of sample quasi-ranges from any population are obtained. These formulae can be used for working downwards with no serious accumulation of rounding errors. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1961
- Accession Number
- AD0259052
Entities
People
- Zakkula Govindarajulu
Organizations
- University of Minnesota