Different estimation methods and joint confidence regions for the parameters of a generalized inverted family of distributions

Yıl 2018, Cilt: 47 Sayı: 1, 203 - 221, 01.02.2018

Wenhao Gui Lei Guo

Öz

In this paper, we deal with the problem of estimating the parameters of a generalized inverted family of distributions. We propose the inverse moment and modified inverse moment estimators of the parameters. The existence and uniqueness of inverse moment and modified inverse moment estimators is derived. Monte Carlo simulations are conducted to compare their performances with maximum-likelihood estimators. Two methods for constructing joint confidence regions for the two parameters are also proposed and their performances are discussed. A numerical example is presented to illustrate the methods.

Anahtar Kelimeler

generalized inverted family of distributions, maximum likelihood estimates, existence and uniqueness, inverse moment estimators, joint confidence regions, Monte Carlo simulation

Kaynakça

• Abouammoh, A. and Alshingiti, A. M. Reliability estimation of generalized inverted expo- nential distribution, Journal of Statistical Computation and Simulation 79(11), 13011315, 2009.
• Arnold, B., Balakrishnan, N. and Nagaraja, H. A First Course in Order Statistics, Clas- sics in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1992.
• Balakrishnan, N. Order statistics from the half logistic distribution, Journal of Statistical Computation & Simulation 20(4), 287-309, 1985.
• Chen, D. G. and Lio, Y. L. Parameter estimations for generalized exponential distribution under progressive type I interval censoring, Computational Statistics & Data Analysis 54(6), 1581-1591, 2010.
• Gupta, R. C., Gupta, P. L. and Gupta, R. D. Modeling failure time data by Lehmann alternatives, Communication in Statistics-Theory and Methods 27(4), 887-904, 1998.
• Gupta, R. D. and Kundu, D. Generalized exponential distributions, Australian & New Zealand Journal of Statistics 41(2), 173-188, 1999.
• Gupta, R. D. and Kundu, D. Generalized exponential distribution: dierent method of estimations, Journal of Statistical Computation & Simulation69(4), 315-337, 2001.
• Gupta, R. D. and Kundu, D. Generalized exponential distribution: existing results and some recent developments, Journal of Statistical Planning & Inference 137(11), 3537-3547, 2007.
• Hinkley, D. On quick choice of power transformation', Journal of the Royal Statistical Society. Series C 26 (1), 67-69, 1977.
• Krishna, H. and Kumar, K. Reliability estimation in generalized inverted exponential dis- tribution with progressively type II censored sample, Journal of Statistical Computation and Simulation 83(6), 1007-1019, 2013.
• Kundu, D. and Pradhan, B. Estimating the parameters of the generalized exponential distri- bution in presence of hybrid censoring, Communications in Statistics: Theory and Methods 38(12), 2030-2041, 2009.
• Nadarajah, S. and Kotz, S. The exponentiated type distributions, Acta Applicandae Math- ematicae 92(2), 97-111, 2006.
• Potdar, K. G. and Shirke, D. T. Inference for the parameters of generalized inverted family of distributions, Probstat Forum 6, 18-28, 2013.
• Raqab, M. M. and Ahsanullah, M. Estimation of the location and scale parameters of gener- alized exponential distribution based on order statistics, Journal of Statistical Computation & Simulation 69(2), 109-123, 2001.
• Ross, S. M. Introduction to probability models(eleventh edition), Academic press, 2014.
• Seo, J.I. and Kang, S.B. Notes on the exponentiated half logistic distribution, Applied Math- ematical Modelling 39(21), 6491-6500, 2015.
• Wang, B. X. Statistical inference for Weibull distribution, Chinese Journal of Applied Prob- ability & Statistics 8(4), 357-364, 1992.