Different estimation methods and joint con dence regions for the parameters of a generalized inverted family of distributions
Different estimation methods and joint con dence regions for the parameters of a generalized inverted family of distributions
In this paper, we deal with the problem of estimating the parameters ofa generalized inverted family of distributions. We propose the inversemoment and modifed inverse moment estimators of the parameters.The existence and uniqueness of inverse moment and modifed inversemoment estimators is derived. Monte Carlo simulations are conductedto compare their performances with maximum-likelihood estimators.Two methods for constructing joint confdence regions for the two parametersare also proposed and their performances are discussed. Anumerical example is presented to illustrate the methods.
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- Wang, B. X. Statistical inference for Weibull distribution, Chinese Journal of Applied Probability
& Statistics 8(4), 357-364, 1992.
- Seo, J.I. and Kang, S.B. Notes on the exponentiated half logistic distribution, Applied Mathematical
Modelling 39(21), 6491-6500, 2015.
- Ross, S. M. Introduction to probability models(eleventh edition), Academic press, 2014.
- Raqab, M. M. and Ahsanullah, M. Estimation of the location and scale parameters of generalized
exponential distribution based on order statistics, Journal of Statistical Computation
& Simulation 69(2), 109-123, 2001.
- Potdar, K. G. and Shirke, D. T. Inference for the parameters of generalized inverted family
of distributions, Probstat Forum 6, 18-28, 2013.
- Nadarajah, S. and Kotz, S. The exponentiated type distributions, Acta Applicandae Mathematicae
92(2), 97-111, 2006.
- Kundu, D. and Pradhan, B. Estimating the parameters of the generalized exponential distribution
in presence of hybrid censoring, Communications in Statistics: Theory and Methods
38(12), 2030-2041, 2009.
- Krishna, H. and Kumar, K. Reliability estimation in generalized inverted exponential distribution
with progressively type II censored sample, Journal of Statistical Computation and
Simulation 83(6), 1007-1019, 2013.
- Hinkley, D. On quick choice of power transformation', Journal of the Royal Statistical
Society. Series C 26 (1), 67-69, 1977.
- 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.
- Gupta, R. D. and Kundu, D. Generalized exponential distribution: diferent method of
estimations, Journal of Statistical Computation & Simulation69(4), 315-337, 2001.
- Gupta, R. D. and Kundu, D. Generalized exponential distributions, Australian & New
Zealand Journal of Statistics 41(2), 173-188, 1999.
- 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.
- 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.
- Balakrishnan, N. Order statistics from the half logistic distribution, Journal of Statistical
Computation & Simulation 20(4), 287-309, 1985.
- Arnold, B., Balakrishnan, N. and Nagaraja, H. A First Course in Order Statistics, Classics
in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM, 3600
Market Street, Floor 6, Philadelphia, PA 19104), 1992.
- Abouammoh, A. and Alshingiti, A. M. Reliability estimation of generalized inverted exponential
distribution, Journal of Statistical Computation and Simulation 79(11), 1301-1315,
2009.