The Asymptotic Frequency Distribution
of Near Extremes
Leon E. Borgman
University of Wyoming
The theorems pertaining to the three possible limiting forms of the exact distribution will be presented in detail. The paper by Gnedenko (1943) will be the basis and starting point for most of the work. His theorems for the largest observation will be systematically extended to include the mth largest observation. No attempt will be made to present an exact translation of his theorems (which are taken from an article in French). Instead, the material will be restated in English in whatever form is deemed to be the most clear and understandable.
- Definition 1
- Definition 2
- Definition 3
- Definition 4
- Definition 5
- Definition 6
- Definition 7
- Definition 8
- Definition 9
- Theorem 1
- Theorem 2
- Theorem 3
- Theorem 4
- Theorem 5
- Theorem 6
- Theorem 7
- Theorem 8
- Theorem 9
- Theorem 10
- Theorem 11
- Theorem 12
- Theorem 13
- Theorem 14
- Theorem 15
- Theorem 16
- Theorem 17
- Theorem 18
- References
- About this document ...
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Borgman's Homepage
3/10/1998