On a Less Cumbersome Method of Estimation of Parameters of Type III Generalized Logistic Distribution by Order Statistics
Keywords:Best linear unbiased estimators, Beta-logistic distribution, Max- imum -likelihood estimators, Moment estimators, Gini's mean dierence, Type III generalized logistic distribution, U-statistics
In this work we have derived appropriate U-statistics from a sample of any size exceeding a specified integer to estimate the location and scale parameters of Type III generalized logistic distribution without the knowledge or by evaluation of the means, variances and co-variances of order statistics of an equivalent sample size arising from the corresponding standard form of distribution. The exact variances and the asymptotic variances of the estimators have been obtained. The efficiency of the obtained estimators relative to some of the standard estimators have been also obtained. An illustration describing the betterness of U-statistics estimation method over the classical maximum-likelihood method is also given.
M. G. BADAR, A. M. PRIEST (1982). Statistical aspects of ber and bundle strength in hybrid composites. In: Hayashi T, Kawata K, Umekawa, S. (Eds.), Progress in Science and Engineering Composites. ICCM-IV, Tokyo, 1129-1136.
N. BALAKRISHNAN (Ed) (1992). Handbook of the Logistic Distribution. Marcel Dekker, New York.
N. BALAKRISHNAN, S. K LEE (1998). Order statistics from the Type III generalized logistic distribution and Applications. Handbook of Statistics, Vol 17 (Eds.,Balakrishnan N, and C. R. Rao), Elsevier Science B.V, Amsterdam.
N. BALAKRISHNAN , M. Y LEUNG (1988). Order statistics from the Type I generalized logistic distribution. Communications in Statistics – Simulation and Computation, vol. 17(1), 25-50.
J. BERKSON (1944). Application of the logistic function to bioassay. Journal of the American Statistical Association, 39, 357-365.
H. A. DAVID, H. N. NAGARAJA (2003). Order Statistics. Third edition, John Wiley and Sons, New York.
R. R. DAVIDSON (1980). Some properties of a family of generalized logistic distribution. In Statistical Climatology, Developments in Atmosphere Sciences, 13 (Eds., S.Ikeda et al.). Elsevier, Amsterdam.
E. J. GUMBEL (1944). Ranges and Midranges: Order statistics from the Type I generalized logistic distribution. The Annals of Mathematical Statistics, 15, 414-422.
W. HOEFFDING (1948). A class of statistics with asymptotically normal distributions. The Annals of Mathematical Statistics, 19, 293-325.
E. H. LLOYD (1952). Least-squares estimation of location and scale parameters using order statistics. Biometrika, 39: 88-95.
N. L. JOHNSON, S. KOTZ, N. BALAKRISHNAN (1994). Continuous Univariate Distributions. Volume I. Second edition, John Wiley and Sons, New York.
N. L. JOHNSON, S. KOTZ, N. BALAKRISHNAN (1995). Continuous Univariate Distributions. Volume 2. Second edition, John Wiley and Sons, New York.
F. R. OLIVER (1982). Notes on the logistic curve for human populations. Journal of the Royal Statistical Society, series A, 145, 359-363.
R. PEARL, L. J REED (1920). On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. Natl. Acad. Sci. 6, 275-288.
R. L. PEARL, L. J REED (1924). Studies in Human Biology. Williams and Wilkins, Baltimore.
P. SAMUEL, P. Y. THOMAS (2003). Estimation of parameters of triangular distribution by order statistics. Calcutta Statistical Association Bulletin, 54, 45-55.
H. SCHULTZ (1930). The standard error of a forecast from a curve. Journal of the American Statistical Association, 25, 139-185.
P. K. SEN (1990). Breakthrough in Statistics, Vol-I. Edited by Kotz, S and Johnson, N. L., Springer, NewYork.
N. V SREEKUMAR, P. Y. THOMAS (2006). Estimation of the scale parameters of linear exponential distribution using order statistics. IAPQR Translations,Vol. 31,No.2, 99-112.
N. V SREEKUMAR, P. Y. THOMAS (2007). Estimation of the parameters of log-gamma distribution using order statistics. Metrika, vol.66, no. 1, 115-127.
N. V SREEKUMAR, P. Y. THOMAS (2008). Estimation of the parameters of Type-I generalized logistic distribution using order statistics. Communications in Statistics-theory and Methods, vol. 37,no.10, 1506-1524.
P. Y. THOMAS (1990). Estimating location and scale parameters of a symmetric distribution by systematic statistics. Journal of the Indian Society of Agricultural Statistics, 42: 250-256.
P. Y. THOMAS, N. V. SREEKUMAR (2004). Estimation of the scale parameters of generalized exponential distribution using order statistics. Calcutta Statistical Association Bulletin, 55, 199-208.
P. Y. THOMAS, N. V. SREEKUMAR (2008). Estimation of location and scale parameters of a distribution by U-statistics based on best linear functions of order statistics. Journal of Statistical Planning and Inference, 138, no. 7: 2190-2200.
P. Y. THOMAS, K. V. BAIJU (2012). Estimation of the scale parameters of Skew- normal distribution usingU-statistics on order statistics. Calcutta Statistical Association Bulletin,64, 1-20.
E.B. WILSON, J. WORCESTER (1943). The determination of L. D. 50 and its sampling error in bioassay. Proc. Natl. Acad. Sci. 29,79-85.