On multivariate weighted distributions

References

• Arnold , B.C. and Nagaraja , H.N. 1991 . On some properties of bivariate weighted distributions . Commun. Statist.-Theory Meth. , 20 ( 5-6 ) : 1853 – 1860 .
   Web of Science ®Google Scholar
• Blumenthal , S. 1967 . Proportional Sampling in Life Length Studies . Technometrics , 9 ( 2 ) : 205 – 218 .
   Web of Science ®Google Scholar
• Esary , J.D. , Proschan , F. and Walkup , D. 1967 . Association of random variables with applications . Ann. Math. Statist. , 38 : 1466 – 1474 .
   Google Scholar
• Fisher , R.A. 1934 . The effect of methods of ascertainment upon the estimation of frequencies . Annals of Eugenics , 6 : 13 – 25 .
   Google Scholar
• Giri , N.C. 1977 . Multivariate Statistical Inference , New York : Academic Press, Inc. .
   Google Scholar
• Gupta , R.C. and Keating , J.P. 1986 . Relations for reliability measures under length-biased sampling . Scand. J. Statist. , 13 : 49 – 56 .
   Web of Science ®Google Scholar
• Gupta , R.C. and Kirmani , S.N.U.A. 1990 . The role of weighted distributions in stochastic modeling . Commun. Statist.-Theory Meth. , 19 ( 9 ) : 3147 – 3162 .
   Web of Science ®Google Scholar
• Jain , K. , Singh , H. and Bagai , I. 1989 . Relations for reliability measures of weighted distributions . Comm. Statist.-Theory Meth. , 18 ( 12 ) : 4393 – 4412 .
   Web of Science ®Google Scholar
• Karlin , S. 1968 . Total Positivity , Vol. 1 , Stanford University Press .
   Google Scholar
• Karlin , S. and Rinott , Y. 1980a . Classes of Orderings of Measures and Related Correlation Inequalities. I.Multivariate Totally Positive Distributions . J. Mult. Anal. , 10 : 467 – 498 .
   Web of Science ®Google Scholar
• Karlin , S. and Rinott , Y. 1980b . Classes of Orderings of Measures and Related Correlation Inequalities. II.Multivariate Reverse Rule Distributions . J. Mult. Anal. , 10 : 499 – 516 .
   Web of Science ®Google Scholar
• Lee , M.L.T. 1985 . Dependence by total positivity . The Annals of Prob. , 13 ( 2 ) : 572 – 582 .
   Web of Science ®Google Scholar
• Mahfoud , M. and Patil , G.P. 1981 . On weighted distributions. In Statistics and Probability: Essays in honor of C.R.Rao, G. Kallianpur
   Google Scholar
• Marshall , A.W. 1975 . “ Multivariate distributions with monotone hazard rate ” . In Reliability and Fault Tree Analysis , 259 – 284 . Philadelphia, PA : Soc. Industrial Appl. Math. .
   Google Scholar
• Patil , G.P. and Ord , J.K. 1976 . On size-biased sampling and related form-invariant weighted distributions . Sankhyā , 38B : 48 – 61 .
   Google Scholar
• Patil , G.P. and Rao , C.R. 1977 . The weighted distributions: A survey and their applications. Applications of Statistics , Edited by: Krishnaiah , P. R. 383 – 405 . North-Holland Publishing Company .
   Google Scholar
• Patil , G.P. and Rao , C.R. 1978 . Weighted distributions and size-biased sampling with applications to wild-life populations and human families . Biometrics , 34 : 179 – 189 .
   Web of Science ®Google Scholar
• Patil , G.P. , Rao , C.R. and Ratnaparkhi , M.V. 1986 . On discrete weighted distributions and their use in model choice for observed data . Comm. Statist.-Theory & Meth. , 15 ( 3 ) : 907 – 918 .
   Web of Science ®Google Scholar
• Rao , C. R. 1965 . On discrete distributions arising out of methods of ascertainment , 320 – 332 . Classical and Contagious Pergamon Press and Statistical Publishing Society .
   Google Scholar
• Rao , C.R. 1973 . Linear Statistical Inference and Its Applications , Second Edition , New Delhi : Wiley Eastern Private Limited .
   Google Scholar
• Rao , C.R. 1985 . “ Weighted distributions arising out of methods of ascertainment: What population does a sample represent? ” . In A celebration of studies, The ISI Centenary Volume , Edited by: Atkinson , A.C. and Fienberg , S. E. 543 – 570 . New York : Springer-Verlag .
   Google Scholar
• Schotz , W.E. and Zelen , M. 1971 . Effect of length-biased sampling on labelled mitotic index waves . J. Theo. Biol. , 32 : 383 – 404 .
   PubMed Web of Science ®Google Scholar
• Whitt , W. 1982 . Multivariate Monotone Likelihood Ratio and Uniform Conditional Stochastic Order . J. Appl. Prob. , 19 : 695 – 701 .
   Web of Science ®Google Scholar