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Some bounds on the distribution functions of linear combinations and applications

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References

  1. Anderson, T. W. (1955). The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities,Proc. Amer. Math. Soc.,6, 170–176.

    Article  MathSciNet  Google Scholar 

  2. Beckenbach, E. and Bellman, R. (1961).Inequalities, Springer-Verlag, New York.

    Google Scholar 

  3. Box, G. E. P. (1954). Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one way classification,Ann. Math. Statist.,25, 290–302.

    MathSciNet  Google Scholar 

  4. Fleiss, J. L. (1971). Distribution of a liner combination of independent Chi squares,J. Amer. Statist. Ass.,66, 142–144.

    Article  MathSciNet  Google Scholar 

  5. Gleser, L. J. (1972). On a new class of bounds for the distribution of quadratic forms in normal variates,J. Amer. Statist. Ass.,67, 655–659.

    Article  MathSciNet  Google Scholar 

  6. Hájek, J. (1962). Inequalities for the generalized student's distribution,Select. Transl. Math. Statist. Prob.,2, 63–74.

    Google Scholar 

  7. Lawton, W. H. (1965). Some inequalities for central and non-central distributions,Ann. Math. Statist.,36, 1521–1525.

    MathSciNet  Google Scholar 

  8. Lehmann, E. L. (1966). Some concepts of dependence,Ann. Math. Statist.,37, 1137–1153.

    MathSciNet  Google Scholar 

  9. Mickey, R. and Brown, M. (1966). Bounds on the distribution functions of Behrens-Fisher statistic,Ann. Math. Statist.,37, 639–642.

    MathSciNet  Google Scholar 

  10. Mudholkar, G. S. (1966). The integral of an invariant unimodal function over an invariant convex set—An inequality and application,Proc. Amer. Math. Soc.,17, 1327–1333.

    Article  MathSciNet  Google Scholar 

  11. Mudholkar, G. S. (1969). A generalized monotone character of distribution functions and moments of statistics from some well-known populationsAnn. Inst. Statist. Math.,21, 277–285.

    MathSciNet  Google Scholar 

  12. Olds, E. G. (1952). A note on the convolution of uniform distribution,Ann. Math. Statist.,23, 282–285.

    MathSciNet  Google Scholar 

  13. Robbins, H. and Pitman, E. J. G. (1949). Applications of the method of mixtures to quadratic forms in normal variates,Ann. Math. Statist.,20, 552–560.

    MathSciNet  Google Scholar 

  14. Welch, B. L. (1956). On linear combinations of several variances,J. Amer. Statist. Ass.,51, 132–148.

    Article  MathSciNet  Google Scholar 

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Presently at Statistics Center, Rutgers University.

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Mudholkar, G.S., Dalal, S.R. Some bounds on the distribution functions of linear combinations and applications. Ann Inst Stat Math 29, 89–100 (1977). https://doi.org/10.1007/BF02532777

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  • DOI: https://doi.org/10.1007/BF02532777

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