Abstract
Based on a small correlations approach, this paper deals with the probability distributions of the order statistics under a general Gaussian model with unequal (positive or negative) correlations. Illustrations are given for the cluster data those follow suitable antedependence models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Albert, J. M. (1992). A corrected likelihood ratio statistic for the multivariate regression model with antedependent errors, Comm. Statist. Theory Methods, 21(7), 1823–1843.
Cochran, W. G. (1977). Sampling Techniques, Wiley, New York.
Ellenberg, J. H. (1973). The joint distribution of the standardized least squares residuals from a general linear regression, J. Amer. Statist. Assoc., 68, 941–943.
Ellenberg, J. H. (1976). Testing for a single outlier from a general linear regression, Biometrics, 32, 637–645.
Gabriel, K. R. (1961). The model of antedependence for data of biological growth, Bull. Inst. Internat. Statist., 33rd Session, 253–264, Paris.
Gabriel, K. R. (1962). Antedependence analysis of an ordered set of variables, Ann. Math. Statist., 33, 201–212.
Greig, M. (1967). Extremes in a random assembly, Biometrika, 54, 273–282.
Gupta, S. S. (1960). Order statistics from the gamma distribution, Technometrics, 2, 243–262.
Gupta, S. S. (1962). Gamma distribution, Contributions to Order Statistics (eds. A. E. Sarhan and B. G. Greenberg), 431–450, Wiley, New York.
Gupta, S. S., Pillai, K. C. S. and Steck, G. P. (1964). On the distribution of linear functions and ratios of linear functions of ordered correlated normal random variables with emphasis on range, Biometrika, 51, 143–151.
Gupta, S. S., Nagel, N. and Panchapakesan, S. (1973). On the order statistics from equally correlated normal random variables, Biometrika, 60(2), 403–413.
Holfman, T. R. and Saw, J. G. (1975). Distribution of the largest of a set of equi-correlated normal variables, Comm. Statist., 4(1), 49–55.
Kenward, M. G. (1987). A method for comparing profiles of repeated measurements, Appl. Statist., 36(3), 296–308.
Owen, D. B. and Steck, G. P. (1962). Moments of order statistics from the equicorrelated multivariate normal distribution, Ann. Math. Statist., 33, 1286–1291.
Prescott, P. (1974). Variances and covariances of order statistics from the gamma distribution, Biometrika, 61(3), 607–613.
Rao, J. N. K., Sutradhar, B. C. and Yuo, K. (1993). Generalized least squares F test in regression analysis with two-stage cluster samples, J. Amer. Statist. Assoc., 88, 1388–1391.
Rawlings, J. O. (1976). Order statistics for a special class of unequally correlated multi-normal variates, Biometrics, 32, 875–887.
Scott, A. C. and Holt, D. (1982). The effect of two-stage sampling on ordinary least squares methods, J. Amer. Statist. Assoc., 77, 848–854.
Wu, C. F. J., Holt, D. and Holmes, D. J. (1988). The effect of two-stage sampling on the F statistics, J. Amer. Statist. Assoc., 83, 150–159.
Author information
Authors and Affiliations
About this article
Cite this article
Saha, K.K., Sutradhar, B.C. On the Distribution of the Extremes of Unequally Correlated Normal Variables with Applications to Antedependent Cluster Data. Annals of the Institute of Statistical Mathematics 51, 301–322 (1999). https://doi.org/10.1023/A:1003810208881
Issue Date:
DOI: https://doi.org/10.1023/A:1003810208881