Properties of Statistics Connected with Minimal Spacing and Record Exceedances
نویسنده
چکیده
This paper attempts to provide an additional insight into properties of exceedances and placement statistics described in Bairamov and Eryılmaz (2000). The importance of these concepts in construction of non-parametric tests of equality (identity) of distributions has been demonstrated by Katzenbeisser (1985), (1986), Matveychuk and Petunin (1990), Johnson and Kotz (1991), (1994), Wesolowsky and Ahsanullah (1998), Bairamov, Gebizlioglu and Kaya (1999). Our study is also related to the theory of invariant confidence intervals which contain the main distributed mass or future observations. Invariant confidence intervals which involve future observations are similar to, but not identical with, the approach of tolerance limits. Tolerance limits are originally introduced by Shewart (1931). Tolerance limits and exceedance statistics are widely discussed be Wilks (1941), Robbins (1944), Gumbel and Shelling (1950), Epstein (1954), Sarkadi (1957), Siddiqui (1977) along with others. Further detailed discussion can be found in
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