References
- Arnold , B. C . 1980 . Distribution-free bounds on the mean of the maximum of a dependent sample . SIAM J. Appl. Math , 38 : 163 – 167 .
- Arnold , B. C and Groeneveld , R. A . 1979 . Bounds on expectations of linear systematic statistics based on dependent samples . Ann. Statist , 7 : 220 – 223 .
- Aven , T. 1985 . Upper (lower) bounds on the mean of the maximum (minimum) of a number of random variables . J. Appl. Probab , 22 : 723 – 728 .
- Balakrishnan , N. and Joshi , P. C . 1985 . Bounds for the mean of se¬cond largest order statistic in large samples . Math. Opera-tionsforsch. u. Statist , 16 : 457 – 464 .
- Beesaek , P. R . 1973 . On bounds for the range of ordered vari¬ ates . Univ, Beograd* Publ, Elektrotehn* Fak* Ser* Mat* Fiz , 16 : 412 – 460 .
- Beesaek , P. K . 1976 . On bounds for rhe range of ordered variates . Aequations Math , 14 : 293 – 301 .
- Boyd , A. V . 1971 . Bounds for order statistics . Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz , 14 : 357 – 360 .
- David , H. A . 1981 . Order Statistics , New York : Wiley .
- David , H. A . 1986 . Inequalities for ordered sums . Ann. Inst. Sta¬tist. Math , 38 : 551 – 555 .
- David , H. A , Harrlpy , H. 0 and Pearson , E. S . 1954 . The distri¬bution of the rarin, in a single normal sample, of range to standard . Biometrika , 41 : 482 – 493 .
- Gravey , A. 1985 . A simple construction of an upper bound for the mean of the maximum of n identically distributed random vari¬ables . Appi , probab , 22 : 844 – 851 .
- Groeneveld , R. A . 1982 . Best bounds for order statistics and their expectations in range and mean units with applications . Commun. Statist.-Theory. Meth , 11 : 1809 – 1815 .
- Hardy , G. H , Littlewood , J. E and Polya , G. 1952 . Inequalities 1st, 2nd Editions , Cambridge University Press .
- Hawkins , D. M . 1971 . On the bounds of the range of the order sta¬tistics . J. Amer. Statist. Ass , 66 : 644 – 645 .
- Hoppe , F. M . 1985 . Iterating Bonferroni bounds . Statist. Probab. Lett , 3 : 121 – 125 .
- Hunter , D. 1977 . Approximate percentage points of statistics ex¬pressible as maxima . TIMS Studies in Management Sciences , 7 : 25 – 36 .
- Joshi , P. C and Balakrishnan , N. 1983 . Bounds for the moments of extreme order statistics for large samples . Math. Operations-forsch. u. Statist., Ser. Statist , 14 : 387 – 396 .
- Lefevre , C. 1986 . Bounds for the expectation of linear combina¬tions of order statistics with application to Pert networks . Stochastic Anal. Appl , 4 : 351 – 356 .
- Mallows , C. L and Richter , D. 1969 . Inequalities of Chebyshev type involving conditional expectations . Ann. Math. Statist , 40 : 1922 – 1932 .
- Marshall , A. W and Olkin , I. 1979 . Inequalities: Theory of Ma¬jor izat ion and Its Applications , New York : Academic Press .
- Nagaraja , H. N . 1981 . Some finite sample results for the selection differential . Ann, lost. Statist, Math , 33 : 437 – 448 .
- Pearson , E. S and Chandra Sekar , C. 1936 . The efficiency of sta¬tistical tools and a criterion for the rejection of outlying ob¬servations . Biometrlka , 28 : 308 – 320 .
- Shapiro , S, S and Wilk , M. B . 1965 . An analysis of variance test for normality . Biometrlka , 52 : 591 – 611 .
- Smith , N. L and Tung , Y. L . 1983 . Inequalities for functions of order statistics under an additive model . Ann. Inst. Statist. Math , 35 : 255 – 265 .
- Sugiura , N. 1962 . On the orthogonal Inverse expansion with an ap¬plication to the moments of order statistics . Osaka J. Math , 14 : 253 – 263 .
- Szekely , G. J and Mori , T, F . 1985 . An extremal property of rectangular distributions . Statist. Probab_ , 3 : 107 – 109 .
- Thomson , G. W . 1955 . Bounds for the ratio of range to standard de¬viation . Biometrlka , 42 : 268 – 269 .
- Tong , Y. L . 1980 . Probability Inequalities in Multivariate , New York : Academi c Press .
- Worsley , K. J . 1982 . An improved Bonferroni inequality and appli¬cations . Biometrlka , 69 : 297 – 302 .
- Yang , J. 1982 . On the variances of median and some other order statistics . Bull. Inst. Math. Acad. Sinica , 10 : 197 – 204 .