Estimation of total time on test transforms and lorenz curves under random censorship

References

• Aalen , O. 1976 . Nonparametric inference in connection with multiple decrement models. . Scand. J. Statist. , 3 : 15 – 27 .
   Google Scholar
• Aly , E.E.A.A. , Csörgo , M. and Horváth , L. 1985 . Strong approximations of the quantile process of the product-limit estimator . J. Multivariate Anal. , 16 : 185 – 210 .
   Web of Science ®Google Scholar
• Barlow , R.E. and Proschan , F. 1977 . “ Asymptotic theory of total time on test processes with applications to life testing ” . In In Multivariate Analysis , Edited by: Krishnaiah , P.R. 227 – 237 . Amsterdam : North-Holland .
   Google Scholar
• Barlow , R.E. and Van zwet , W.R. 1970 . “ Asymptotic properties of isotonic estimators for the generalized failure rate function ” . In In Nonparametric Techniques in Statistical Inference , Edited by: Puri , M.L. 159 – 173 . Cambridge unviersity Press .
   Google Scholar
• Breslow , N. and Crowley , J. 1974 . A large sample study of the life table and product limit estimates under random censorship . Ann. Statist. , 2 : 437 – 453 .
   Web of Science ®Google Scholar
• Burke , M.D. , Csörgo , S. and Horváth , L. 1981 . Strong approximations of some biometric estimates under random censorship . Zeit. Wahrscheinlichkeitsh. , 56 : 87 – 112 .
   Web of Science ®Google Scholar
• CHANDRA, M. and SINGPURWALLA, N.D. (1978). The Gini index, the Lorenz curve, and the total time on test transforms, Technical Report T-368, The George Washington Univ.
   Google Scholar
• Csörgo , M. 1983 . “ CMBS-NSF Regional Conference Series in Applied Mathematics ” . In Quantile Processes with Statistical Applications. , Vol. 42 , Philadelphia : SIAM .
   Google Scholar
• Csörgo , M. , Csörgo , S. and Horváth , L. 1986 . “ Lecture Notes in Statistics ” . In An Asymptotic Theory for Empirical Reliability and Concentration Processes. , Vol. 33 , New York : Springer-Verlag .
   Google Scholar
• Csörgo , M. , Csörgo , S. , Horváth , L. and Mason , D.M. 1986 . Weighted empirical and quantile processes. . Ann. Probab. , 14 : 31 – 85 .
   Web of Science ®Google Scholar
• Csörgo , M. , Horváth , L. and Yalovski , M. 1975 . “ Applications of characterizations in the area of goodness-of-fit. ” . In In Statistical Distributions in Scientific Work , Edited by: Ord , J.K. Vol. 2 , 79 – 90 . Dordrecht : D. Reidel .
   Google Scholar
• Csörgo , S. and Horváth , L. 1982 . Statistical inference from censored samples. . Alkalmaz. Mat. Lapok , 8 : 1 – 89 .
   Google Scholar
• Csörgo , S. and Horváth , L. 1983 . The rate of strong uniform consistency for the product-limit estimator . Zeit. Wahrscheinlichkeitsth , 62 : 411 – 426 .
   Web of Science ®Google Scholar
• Doksum , K.A. and Yandell , B.S. 1984 . “ Testing for exponentiality ” . In In Handbook of Statistics , Edited by: Sen , P.K. Vol. 4 , 579 – 611 . Amsterdam : North-Holland .
   Google Scholar
• Efron , B. 1967 . The two-sample problem with censored data. . Proc. 5th Berkeley Symp. Math. Statist. Prob. , 4 : 831 – 853 .
   Google Scholar
• Ghorai , J. , Susarla , A. , Susarla , V. and Van ryzin , J. 1982 . “ Nonparametric estimation of mean residual life time with censored data. ” . In In Colloquia Mathematica Societatis János Bolyai 32. Nonparametric Statistical Inference , Edited by: Vincze , I. 269 – 291 . Amsterdam : North-Holland .
   Google Scholar
• Gill , R.D. 1980 . Censoring and Stochastic Integrals. , Vol. 124 , Amsterdam : Mathematical Centre Tracts .
   Google Scholar
• Gill , R.D. 1983 . Large sample behaviour of the product-limit estimator on the whole line . Ann. Statist. , 11 : 49 – 58 .
   Web of Science ®Google Scholar
• Gill , R.D. 1986 . The total time on test plot and cumulative total time on test statistic for a counting process . Ann. Statist. , 11
   Google Scholar
• Goldie , C.M. 1977 . Convergence theorems for empirical Lorenz curves and their inverses . Adv. Appl. Probab. , 9 : 765 – 791 .
   Web of Science ®Google Scholar
• Horváth , L. 1980 . Dropping continuity and independence assumptions in random censorship models. . Studia Sci. Math. Hungar. , 15 : 381 – 389 .
   Google Scholar
• Ito , K. and Mckean , H.P.,Jr. 1966 . Diffusion Processes and their Sample Paths. , Berlin : Springer .
   Google Scholar
• Kaplan , E.L. and Meier , P. 1958 . Nonparametric estimation from incomplete observations. . J. Amer. Statist. Assoc. , 53 : 457 – 481 .
   Web of Science ®Google Scholar
• Klefsjö , B. 1982 . On aging properties and total time on test transforms. . Scand. J. Statist. , 9 : 37 – 41 .
   Web of Science ®Google Scholar
• Langberg , N.A. , León , R.V. and Proschan , F. 1980 . Characterization of nonparametric classes of life distributions. . Ann. Probab. , 8 : 1163 – 1170 .
   Web of Science ®Google Scholar
• Rényi , A. 1973 . On a group of problems in the theory of order statistics. . Selected Transl. in Math. Statist. and Probab. Amer. Math. Soc. , 13 : 289 – 298 .
   Google Scholar
• Sendler , W. 1982 . On functionals of order statistics . Metrika , 29 : 19 – 54 .
   Google Scholar
• Susarla , V. and Van ryzin , J. 1980 . Large sample theory for an estimator of the mean survival time for censored samples. . Ann. Statist. , 8 : 1001 – 1016 .
   Web of Science ®Google Scholar
• Yang , G.L. 1977 . Life expectancy under random censorship. . Stochastic Process. Appl , 6 : 33 – 39 .
   Google Scholar