Estimation of the Parameters of Type-I Generalized Logistic Distribution Using Order Statistics

References

• Balakrishnan , N. , Leung , M. Y. ( 1988a ). Order statistics from the type I generalized exponential distribution . Commun. Statist. Simul. Computat. 17 : 25 – 50 .
   Web of Science ®Google Scholar
• Balakrishnan , N. , Leung , M. Y. ( 1988b ). Means, variances and covariances of order statistics, BLUE's for the type I generalized logistic distribution and some applications . Commun. Statist. Simul. Computat. 17 : 51 – 84 .
   Web of Science ®Google Scholar
• Balakrishnan , N. , Cohen , A. C. ( 1991 ). Order Statistics and Inference: Estimation Methods . San Diego : Academic Press .
   Google Scholar
• Balakrishnan , N. , Rao , C. R. ( 1998a ). Handbook of Statistics—Order Statistics: Theory and Methods . Vol. 16 . Amsterdam : Elsevier Science B.V .
   Google Scholar
• Balakrishnan , N. , Rao , C. R. ( 1998b ). Handbook of Statistics — Order Statistics: Applications . Vol. 17 , Amsterdam : Elsevier Science B.V .
   Google Scholar
• Berkson , J. ( 1944 ). Application of the logistic function to bio-assay . J. Amer. Statist. Assoc. 39 : 357 – 365 .
   Web of Science ®Google Scholar
• Berkson , J. ( 1951 ). Why I prefer logits to probits . Biometrics 7 : 327 – 339 .
   Web of Science ®Google Scholar
• Berkson , J. (1953). A statistically precise and relatively simple method of estimating the bio-assay and quantal response, based on the logistic function. J. Amer. Statist. Assoc. 48:565–599.
   Web of Science ®Google Scholar
• Birnbaum , A. , Dudman , J. ( 1963 ). Logistic order statistics . Ann. Mathemat. Statist 34 : 658 – 663 .
   Google Scholar
• David , H. A. , Nagaraja , H. N. ( 2003 ). Order Statistics. , 3rd ed. New York : John Wiley & Sons .
   Google Scholar
• Erkelens , J. ( 1968 ). A method of calculation for the logistic curve . Statistica Neerlandica 22 : 213 – 217 .
   Google Scholar
• Gupta , S. S. , Shah , B. K. ( 1965 ). Exact moments and percentage points of the order statistics and the distribution of the range from the logistic distribution . Ann. Mathemat. Statist. 36 : 907 – 920 .
   Google Scholar
• Gupta , S. S. , Qureishi , A. S. , Shah , B. K. ( 1967 ). Best linear unbiased estimators of the parameters of the logistic distribution using order statistics . Technometrics 9 : 43 – 56 .
   Web of Science ®Google Scholar
• Hoeffding , W. ( 1948 ). A class of statistics with asymptotically normal distributions . Ann. Mathemat. Statist. 19 : 293 – 325 .
   Google Scholar
• Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1995 ). Continuous Univariate Distributions . Vol. 2 . New York : Wiley .
   Google Scholar
• Lawless , J. F. ( 1982 ). Statistical Models and Methods for Lifetime Data . New York : John Wiley .
   Google Scholar
• Lloyd , E. H. ( 1952 ). Least-squares estimation of location and scale parameter using order statistics . Biometrika 39 : 88 – 95 .
   Web of Science ®Google Scholar
• Mann , N. R. , Schafer , R. E. , Singerpurwalla , N. D. ( 1974 ). Methods of Statistical Analysis of Reliability and Life time Data . New York : John Wiley .
   Google Scholar
• Nair , U. S. ( 1936 ). The standard error of Gini's mean difference . Biometrika 28 : 428 – 436 .
   Web of Science ®Google Scholar
• Samuel , P. , Thomas , P. Y. ( 2003 ). Estimation of the parameters of triangular distribution by order statistics . Calcutta Statist. Assoc. Bull. 54 : 45 – 55 .
   Google Scholar
• Sarhan , A. E. , Greenberg , B. G. ( 1962 ). Contributions to Order Statistics . New York : Wiley .
   Google Scholar
• Serfling , R. J. ( 1980 ). Approximation Theorems of Mathematical Statistics . New York : John Wiley & Sons .
   Google Scholar
• Shah , B. K. ( 1966 ). On the bivariate moments of order statistics from logistic distribution . Ann. Mathemat. Statist. 37 : 1002 – 1010 .
   Google Scholar
• Shah , B. K. ( 1970 ). A note on moments of logistic order statistics . Ann. Mathemat. Statist. 41 : 2151 – 2152 .
   Google Scholar
• Tarter , M. E. , Clark , V. A. ( 1965 ). Properties of the median and other order statistics of logistic variates . Ann. Mathemat. Statist. 36 : 1779 – 1786 .
   Google Scholar
• Thomas , P. Y. , Sreekumar , N. V. ( 2004 ). Estimation of the scale parameter of generalized exponential distribution using order statistics . Calcutta Statist. Assoc. Bull. 55 : 199 – 208 .
   Google Scholar
• Thomas , P. Y. , Sreekumar , N. V. ( 2007 ). Estimation of the location and scale parameters of a distribution by U-statistics based on best linear functions of order statistics. (Communicated for publication) .
   Google Scholar