Muth Distribution and Estimation of a Parameter Using Order Statistics
Keywords:Order statistics, Muth distribution, Best linear unbiased estimator, U-statistics
In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration. We have derived the best linear unbiased estimator (BLUE) of the scale parameter of the Muth distribution based on order statistics for some known values of the shape parameter.We have further estimated the scale parameter of Muth distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency of the BLUE relative to the usual unbiased estimator has been also evaluated. An illustration describing the performance of U-statistics estimation method when compared with the classical maximum likelihood method is also given.
H. A. DAVID, H. N. NAGARAJA (2003). Order Statistics. John Wiley and Sons, New York, third ed.
B. GOMPERTZ (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115, pp. 513–583.
W. HOEFFDING (1948). A class of statistics with asymptotically normal distribution. The Annals of Mathematical Statistics, 19, no. 3, pp. 293–325.
M. R. IRSHAD, R.MAYA (2018). On a less cumbersome method of estimation of parameters of Lindley distribution by order statistics. Statistics in Transition New Series, 19, pp. 597–620.
M. R. IRSHAD, N. K. SAJEEVKUMAR (2016). Estimating the mean of the logistic distribution with known coefficient of variation by U-statistics. Thailand Statistician, 14, pp. 117–128.
A. G. LAURENT (1975). Failure and mortality from wear and ageing - The Teissier model. In G. PATIL, S. KOTZ, J. ORD (eds.), A Modern Course on Statistical Distributions in Scientific Work, Springer, Heidelberg, vol. 17, pp. 301–320.
L. M. LEEMIS, J. T. MCQUESTON (2008). Univariate distribution relationships. The American Statistician, 62, no. 1, pp. 45–53.
E. H. LLOYD (1952). Least-squares estimation of location and scale parameters using order statistics. Biometrika, 39, pp. 88–95.
E. J.MUTH (1977). Reliability models with positive memory derived from the mean residual life function. The Theory and Applications of Reliability, 2, pp. 401–435.
J. PEDRO, M. D. JIMÉNEZ GAMERO, V. ALBA-FERNÁNDEZ (2015). On the Muth distribution. Mathematical Modelling and Analysis, 20, pp. 291–310.
H. RINNE (1981). Estimating the lifetime distribution of private motor-cars using prices of used cars-the Teissier model. Statistiks Zwischen Theorie und Praxis, pp. 172–184.
V. K. ROHATGI, A. K. EHSANES SALEH (2009). An Introduction to Probability and Statistics. Wiley.
N. K. SAJEEVKUMAR, M. R. IRSHAD (2013). Estimation of the mean of the Normal distribution with known coefficient of variation by U-statistics. IAPQR Transactions, 38, pp. 51–65.
R. J. SERFLING (1980). Approximation Theorems of Mathematical Statistics. John Wiley and Sons, New York.
N. V. SREEKUMAR, P. Y. THOMAS (2007). Estimation of the parameters of log-gamma distribution using order statistics. Metrika, 66, pp. 115–127.
A. STUART (1954). The correlation between variate-values and ranks in samples from a continuous distribution. British Journal of Statistical Psychology, 7, no. 1, pp. 37–44.
G. TEISSIER (1934). Recherches sur le vieillissement et sur les lois de la mortalité. II. essai d’interprétation genérale des courbes de survie. Annales de Physiologie et de Physicochimie Biologique, 10, pp. 260–284.
P.Y.THOMAS, R. PRIYA (2015). Ona less cumbersome method of estimation of parameters of type III generalized logistic distribution by order statistics. Statistica, 75, pp. 291–312.
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, pp. 2190–2200.
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