On approximating probability distributions of a statistic of brown-forsythe from normal and non-normal universes

References

• Box , G.E.P. and Tiao , C.H. 1968 . A Bayesian approach to some outlier problems . Biometrika , 55 : 119 – 129 .
   PubMed Web of Science ®Google Scholar
• Brown , M.B. and Forsythe , A.B. 1974a . The ANOVA and mutiple comparisons for data with heterogeneous variances . Biometrics , 30 : 719 – 724 .
   Web of Science ®Google Scholar
• Brown , M.B. and Forsythe , A.B. 1974b . The small sample behavior of some statistics which test the equality of several means . Technometrics , 16 : 129 – 132 .
   Web of Science ®Google Scholar
• Davis , A.W. 1976 . Statistical distributions in univariate and multivariate Edgeworth populations . Biometrika , 63 : 661 – 670 .
   Web of Science ®Google Scholar
• Donaldson , T.S. 1968 . Robustness of the F-test to errors of both kinds of the correlation between the numerator and denominator of the F-ratio . Jour. Amer. Statist. Assoc , 63 : 660 – 667 .
   Web of Science ®Google Scholar
• Fisher , R.A. 1928 . Moments and product moments of sampling distributions . Proc. London Math.Soc , 30 : 199 – 238 .
   Google Scholar
• Gideon , R.A. 1977 . Some alternative expansions of the distribution function of a noncentral chi-squared random variable . SIAM J Math. Analysis , 8 : 100 – 110 .
   Web of Science ®Google Scholar
• Hyrenius , H. 1950 . Distribution of Student Fisher’s t in samples from compound normal distribution . Biometrika , 37 : 429 – 442 .
   PubMed Web of Science ®Google Scholar
• Hyrenius , H. 1952 . Sampling from bivariate nonnormal universes by means of compound normal distributions . Biometrika , 39 : 238 – 246 .
   Google Scholar
• Kendall , M.G. and Stuart , A. 1958 . The Advanced Theory of Statistics , Vol. 1 , London : Griffin .
   Google Scholar
• Kotz , S. , Johnson , N.L. and Boyd , D.W. 1967a . Series representations of distributions of quadratic forms in normal variables I. Central case . Ann. Math. Statist , 38 : 823 – 837 .
   Google Scholar
• Kotz , S. , Johnson , N.L. and Boyd , D.W. 1967b . Series representations of distributions of quadratic forms in normal variables II. Non-cenirai case . Ann. Math. Statist , 38 : 838 – 848 .
   Google Scholar
• Lee , A.F.S. and Gurland , J. 1977 . One-sample t-test when sampling from a mixture of normal distributions . Ann. Statist , 5 : 803 – 807 .
   Web of Science ®Google Scholar
• Pearson , E.S. and Tiku , M.L. 1970 . Some notes on the relationship between the distributions of central and noncentral F . Biometrika , 51 : 175 – 177 .
   Web of Science ®Google Scholar
• Rao , C.R. 1973 . Linear Statistical Inference and its Applications , New York : John Wiley and Sons .
   Google Scholar
• Scheffe , H. 1959 . The Anahvs of Variances , New York : John Wiley and Sons .
   Google Scholar
• Searlc , S.R. 1971 . Linear Models , New York : John Wiley and Sons .
   Google Scholar
• Subrahmaniam , K. 1972 . On quadratic forms mixtures of tuo normal populations . S.Amer.Statist. J , 6 : 103 – 120 .
   Google Scholar
• Subrahmamam , K. and Messen , J.Y. 1975 . On the robustness ol some tests of significance in sampling from a compound normal population . Jour. Amer. Siatist. Assoc , 70 : 435 – 438 .
   Google Scholar
• Tan , W.Y. 1977 . On the distribution of second degree polynomial in normal random variables . Canadian Jour. Statist , 5 : 241 – 250 .
   Google Scholar
• Tan , W.Y. 1982 . Sampling distributions and robustness of t F and variance ratio in two samples and ANOVA models with respect to departure from normality . Comm. Statistics All , 5 To appear in Special Issue: Robust Inferences
   Google Scholar
• Tan , W.Y. and Chang , W.C. 1972 . Convolution approach to the analysis of quantitative characters in self-fertilized populations . Biometrics , 28 : 1073 – 1090 .
   Web of Science ®Google Scholar
• Tan , W.Y. and Cheng , S.S. 1981 . Cumulants of bilinear forms and quadratic forms and its applications . Comm. in Statist , A10 : 283 – 298 .
   Google Scholar
• Tan , W.Y. and Wong , S.P. 1977 . On the Roy-Tiku approximation to the distribution of sample variance from nonnormal universe . Jour. Amer Statist Assoc , 72 : 875 – 881 .
   Web of Science ®Google Scholar
• Tan , W.Y. and Wong , S.P. 1978 . On approximating the central and noncentral multivariate gamma distributions . Comm. in Statist , B7 : 227 – 243 .
   Google Scholar
• Tan , W.Y. and Wong , S.P. 1980 . On approximating the null and nonnull distributions of the F-ratio in unbalanced random effect models from nonnormal universes . Jour. Amer. Statist. Assoc , 75 : 655 – 662 .
   Web of Science ®Google Scholar
• Tiao , C.H. and Ali , M.M. 1971 . Effect of nonnormality on inference about variance components . Technometrics , 13 : 625 – 650 .
   Google Scholar
• Tiku , M.L. 1964 . Approximating the general nonnormal variance-ratio sampling distributions . Biometrika , 51 : 83 – 95 .
   Web of Science ®Google Scholar
• Tiku , M.L. 1965 . Laguerre series forms of noncentral x 2 and F-distributions . Biometrika , 52 : 415 – 427 .
   PubMed Web of Science ®Google Scholar
• Tiku , M.L. 1971 . Power function of the F-test under nonnormal situations . J. Amer. Statist. Assoc , 66 : 913 – 916 .
   Web of Science ®Google Scholar
• Tiku , M.L. 1975 . “ Laguerre series forms of the distributions of classical test-statistics and their robustness in nonnormal situations ” . In Applied Statistics , Edited by: Gupta , R.P. N.Y : American Elsevier Pub.Co .
   Google Scholar