Estimation and hypothesis testing for a nonnormal bivariate distribution with applications

Mathematical and Computer Modelling

Volumn 32, Issue 1-2, 2000, Pages 53-67

  Vaughan, D C ^a   Tiku, M L ^b  

^a WILFRID LAURIER UNIVERSITY   (Canada)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

Correlation coefficient; Extreme value; Maximum likelihood; Modified maximum likelihood; Weibull

Indexed keywords

EID: 0034234118     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(00)00119-9     Document Type: Article

References (36)

1. T.P. Hutchinson and C.D. Lai, Continuous Bivariate Distributions Emphasising Applications, Rumsby Scientific, Adelaide, (1990).
2. V.D. Barnett, Order statistic estimators of the location of the Cauchy distribution, J. Amer. Statist. Assoc. 61, 1205-1218, (1966).
3. V.D. Barnett, Evaluation of the maximum likelihood estimator when the likelihood equation has multiple roots, Biometrika 53, 151-165, (1966).
4. K.R. Lee, C.H. Kapadia and B.B. Dwight, On estimating the scale parameter of the Rayleigh distribution from doubly censored samples, Statist. Hefte. 21, 14-29, (1980).
5. D.C. Vaughan, On the Tiku-Suresh method of estimation, Commun. Stat.-Theory Meth. 21, 451-469, (1992).
6. M.L. Tiku, Estimating the mean and standard deviation from a censored normal sample, Biometrika 54, 155-165, (1967).
7. M.L. Tiku, Estimating the parameters of normal and logistic distributions from censored samples, Austral. J. Statist. 10, 64-74, (1968).
8. M.L. Tiku, Robustness of MML estimators based on censored samples and robust test statistics, J. Seat. Plann. Inf. 4, 123-143, (1980).
9. M.L. Tiku and R.P. Suresh, A new method of estimation for location and scale parameters, J. Stat. Plann. Inf. 30, 281-292, (1992).
10. Md.A.K. Saleh, Book review of Order Statistics and Inference, Metrika 41, 307-309, (1994).
11. M.L. Tiku, Monte Carlo study of some simple estimators in censored normal samples, Biometrika 57, 207-211, (1970).
12. G.K. Bhattacharyya, The asymptotics of maximum likelihood and related estimators based on type II censored data, J. Amer. Stat. Assoc. 80, 398-404, (1985).
13. M.L. Tiku, W.Y. Tan and N. Balakrishnan, Robust Inference, Marcel Dekker, New York, (1986).
14. W.B. Smith, C.D. Zeiss and G.W. Syler, Three parameter lognormal estimation from censored data, J. Ind. Statist. Assoc. 11, 15-31, (1973).
15. W.Y. Tan, On Tiku's robust procedure-A Bayesian insight, J. Statist. Plann. Inf. 11, 329-340, (1985).
16. H. Schneider, Truncated and Censored Samples for Normal Populations, Marcel Dekker, New York, (1986).
17. J. Lieblien, On the exact evaluation of the variances and covariances of order statistics in samples from the extreme value distribution, Ann. Math. Stat. 24, 282-287, (1953).
18. J.S. White, The moments of the log-Weibull order statistics, Technometrics 11, 373-386, (1969).
19. G. Blom, Statistical Estimates and Transformed Beta-Variables, Almqvist and Wiksells, Uppsala, (1958).
20. W.R. Van Zwet, Convex Transformations of Random, Variables, Mathematical Centre Tracts 7, Mathematisch Centrum, Amsterdam, (1964).
21. M.L. Tiku and N.S. Kambo, Estimation and hypothesis testing for a new family of bivariate nonnormal distributions, Commun. Stat.-Theory Meth. 21, 1683-1705, (1992).
22. W. Hoeffding, On the distribution of the expected values of the order statistics, Ann. Math. Stats. 24, 93-100, (1953).
23. M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, Vol. 2, Fourth edition, Griffin, London, (1979).
24. M.L. Tiku, Testing linear contrasts of means in experimental design without assuming normality and homogeneity of variances, (Invited paper), Biometrical J. 24, 613-627, (1982).
25. J.F. Lawless, Statistical Models and Methods for Lifetime Data, John Wiley, New York, (1982).
26. M.L. Tiku, Laguerre series forms of noncentral x2 and F distributions, Biometrika 52, 415-427, (1965).
27. A.J. Gross and V.A. Clark, Survival Distributions, John Wiley, New York, (1975).
28. M.L. Tiku, Goodness-of-fit statistics based on the spacings of complete or censored samples, Austral. J. Statist. 22, 260-275, (1980).
29. D. Dyer and M.S. Harbin, An empirical power study of multi-sample tests of exponentiality, J. Stat. Comp. Simul. 12, 277-291, (1981).
30. M.L. Tiku and M. Singh, Testing the two parameter Weibull distribution, Commun. Stat.-Theory Meth. 10, 907-918, (1981).
31. E.S. Pearson and H.O. Hartley, Biometrika Tables for Statisticians, Vol. II, Cambridge University Press, Cambridge, (1976).
32. M.L. Tiku and P.S. Gill, Modified maximum likelihood estimators for the bivariate normal based on Type II censored samples, Commun. Stat.-Theory Meth. 18, 3505-3518, (1989).
33. P.S. Gill, M.L. Tiku and D.C. Vaughan, Inference problems in life testing under multivariate normality, J. Applied Statistics 17, 133-147, (1990).
34. I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products, Fifth edition, (Edited by A. Jeffrey), Academic Press, New York, (1994).
35. K.V. Mardia, Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies, Sankhya 36, 115-128, (1974).
36. H.A. David and R.A. Groeneveld, Measures of local variation in a distribution: Expected length of spacings and variances of order statistics, Biometrika 69, 227-232, (1982).