The Probability of Large Deviations Forthe Sum Functions of Spacings
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چکیده
Let 0= U0,n ≤ U1,n ≤ ··· ≤ Un−1,n ≤ Un,n = 1 be an ordered sample from uniform [0,1] distribution, and Din = Ui,n −Ui−1,n, i = 1,2, . . . ,n; n = 1,2, . . . , be their spacings, and let f1n, . . . , fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)= f1n(nD1n) + ···+ fnn(nDnn) are proved. Application of these theorems for determination of the intermediate efficiencies of the tests based on Rn(D)-type statistic is presented here too.
منابع مشابه
The probability of large deviations for the sum functions of spacings
Let 0= U0,n ≤ U1,n ≤ ··· ≤ Un−1,n ≤ Un,n = 1 be an ordered sample from uniform [0,1] distribution, and Din = Ui,n −Ui−1,n, i = 1,2, . . . ,n; n = 1,2, . . . , be their spacings, and let f1n, . . . , fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)= f1n(nD1n) + ···+ fnn(nDnn) are proved. Applicati...
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Let 0= U0,n ≤ U1,n ≤ ··· ≤ Un−1,n ≤ Un,n = 1 be an ordered sample from uniform [0,1] distribution, and Din = Ui,n −Ui−1,n, i = 1,2, . . . ,n; n = 1,2, . . . , be their spacings, and let f1n, . . . , fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)= f1n(nD1n) + ···+ fnn(nDnn) are proved. Applicati...
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