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http://hdl.handle.net/11718/3538
Title: | Limiting distributions of kolmogorov-smirnov type statistics under the alternative |
Authors: | Raghavachari, M. |
Issue Date: | 31-Jan-1973 |
Citation: | Annals of Statistics, I, 1 (Jan 1973), 67-73 |
Abstract: | Let XI, X2, - - - be a sequence of independent and identically distributed random variables with the common distribution being uniform on [0, 1]. Let Y1, Y2, * * - be a sequence of i.i.d. variables with continuous cdf F(t) and with [0, 1] support. Let Fn(t, wo) denote the empirical distribution function based on Yi(w), * * *, Yn(w) and let Gm(t, w) the empirical cdf pertaining to X1(@), * * *, Xm(a(). Let supogt?j JF(t) - tj = i and Dn = supostsl i Fn(t, o1) - tl. The limiting distribution of ni(Dn - i) is obtained in this paper. The limiting distributions under the alternative of the corresponding one-sided statistic in the one-sample case and the corresponding Smirnov statistics in the two-sample case are also derived. The asymptotic distributions under the alternative of Kuiper's statistic are also obtained. |
URI: | http://hdl.handle.net/11718/3538 |
Appears in Collections: | Journal Articles |
Files in This Item:
File | Description | Size | Format | |
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LimitingDistributionsofKolmogorov.pdf Restricted Access | 605.3 kB | Adobe PDF | View/Open Request a copy |
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