Simultaneous Linear Estimation of the Location and Scale Parameters of the Extreme-Value Distribution Using Selected Order Statistics from Doubly Censored Samples.
Abstract
The location and scale parameters of the extreme-value distribution (Type I) may be estimated by applying general least-square theory to an ordered sample. The resulting estimators are linear, unbiased and of minimum variance among linear unbiased estimators. The procedure is also applicable to censored samples where the R sub 1 smallest and R sub 2 largest observations are missing leaving N - (R sub 1 + R sub 2) = M observations available. The M-order-static-estimator variances for the extreme-value distribution are tabulated for N = 3(1)18, M = 2(1)N. Since certain observations contain more information about distribution parameters than others, efficient estimators may be obtained by using only L of the M available observations. The coefficients of linear estimation based on selected order statics, together with efficiencies relative to M-order-statistic estimators, are tabulated for N = 3(1)18, M = 2(1)N, L = 2(1)m where m is either M or the value of L giving a 99.0% efficient estimator, whichever is reached first. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0849869
Entities
People
- William F. Fratzke
Organizations
- Air Force Institute of Technology