International Journal of Information Technology and Computer Science (IJITCS)
IJITCS Vol. 6, No. 3, 8 Feb. 2014
Cover page and Table of Contents: PDF (size: 316KB)
Minimax Estimation of the Parameter of Exponential Distribution based on Record Values
Full Text (PDF, 316KB), PP.47-53
Views: 0 Downloads: 0
Author(s)
Lanping Li
1,*
Index Terms
Bayes Estimator, Minimax Estimator, Squared Log Error Loss, Entropy Loss, Record Value
Abstract
Bayes estimators of the parameter of exponential distribution are obtained with non-informative quasi-prior distribution based on record values under three loss functions. These functions are weighted squared error loss, square log error loss and entropy loss functions. Finally the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Comparisons in terms of risks with the estimators of parameter under three loss functions are also studied.
Cite This Paper
Lanping Li, "Minimax Estimation of the Parameter of Exponential Distribution based on Record Values", International Journal of Information Technology and Computer Science(IJITCS) vol.6, no.3, pp.47-53, 2014. DOI:10.5815/ijitcs.2014.03.06
Reference
[1]Arnold B C , Balakrishnan,N , Nagaraja,H N. Records[M]. John Wiley &Sons, NewYork,1998
[2]Raqab, M Z. Inferences for generalized exponential distribution based on records statistics[J]. J.Statist.Plan. Inference, 2002, 104(2): 339-350
[3]Jaheen, Z F.Empirical Bayes analysis of record statistics based on LINEX and quadratic loss functions[J]. Computers and Mathematics with Applications, 2004,47:947-954
[4]Ahmadi , J, Doostparast, M and Parsian, A. Estimation and prediction in a two parameter exponential distribution based on k-record values under LINEX loss function[J]. Comm. Statist. Theory and Methods, 2005, 34:795-805.
[5]Bain, L J. Statistical Analysis of Reliability and Life Testing Models[M]. Marcer Dekker, New York, 1978.
[6]Chandrasekar, B, Alexander,T L and Balakrishnan, N. Equivariant estimation for parameters of exponential distributions based type-II progressively censored samples[J]. Communications in Statistics. Theory and Methods, 2002, 31(1):1675-1686.
[7]Varian, H R. A Bayesian approach to real estimate assessment[A]. In:Studies in Bayesian Econometrics and statistics in Honor of L.J.Savage, Amsterdam,North Holland, 1975,195-208,.
[8]Zellner, A. Bayesian estimation and prediction using asymmetric loss function[J]. Journal of American statistical Association,1986, 81:446-451.
[9]Podder, C K, Roy, M K , Bhuiyan, K J and Karim, A. Minimax estimation of the parameter of the Pareto distribution for quadratic and MLINEX loss functions[J]. Pak. J. Statist. , 2004, 20(1):137-149.
[10]Kiapoura A, Nematollahib N. Robust Bayesian prediction and estimation under a squared log error loss function[J].Statistics & Probability Letters,2011, 81(11):1717-1724
[11]Mahmoodi, E, Farsipour,N S.Minimax estimation of the scale parameter in a family of transformed chi-square distributions under asymmetric square log error and MLINEX loss functions[J]. Journal of sciences, Islamic republic of Islamic, 2006, 17(3):253-258.
[12]Dey,D K , Ghosh, M and Srinivasan, C. Simultaneous estimation of parameters under entropy loss[J],J. Statist. Plan. and Infer.,1987,15:347-363
[13]Singh S K , Singh U , Kumar D.Bayesian estimation of the exponentiated Gamma parameter and reliability function under asymmetric loss function.[J] REVSTAT, 2011, 9(3): 247–260
[14]Li Jin Ping, Ren Hai Ping. Estimation of one-parameter exponential family under entropy loss function based on record values[J]. International Journal of Engineering and Manufacturing, 2012,4: 84-92.