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Details for article 4 of 10 found articles
| Title: |
Evaluation of some steck determinants with applications |
| Author: |
Steck, G.P. |
| Appeared in: |
Communications in statistics |
| Paging: | Volume 3 (1974) nr. 2 pages 121-138 |
| Year: |
1974 |
| Contents: |
Let [image omitted] and [image omitted] be the order statistics from two independent samples of iid random variables with common continuous distribution function F. Let [image omitted] denote the ordered combined sample and let Ribe the rank of Xiamong the Z's. Steck (1969) proved that for non-decreasing sequences of integers {b1}and {ci} [image omitted] where [image omitted] The proof was overly complicated and later Mohanty (1971), Pitman (1972) and Sarkadi (1973) gave simpler proofs. In this paper wer evaluate certain of these determd nants assumding n = mb and use them to obtain expressions for the distribution of the two-sided Smirnov statistic and the doubly truncated one-sided Smirnov statistic. In the process we also rederive the combinatorial expressions found by Korolyuk (1955) and Gnedenko and Rvaceva (1952) for the distributions of the one and two-sided Smirnov statistics The principal technique for evaluating these determinants is to modify them by repeated use of Vandermonde type convolution formulae until they become recognizable as a determinant whose value is known. In evaluating the two-sided Smirnov distribution we shall also have occasion to use some results from the theroy of Lagrange series. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 4 of 10 found articles
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