On estimation of the exponentiated Pareto distribution under different sample schemes. (English) Zbl 1230.62006
Summary: Bayes and classical estimators have been obtained for a two-parameter exponentiated Pareto distribution when samples are available from complete, type I and type II censoring schemes. Bayes estimators have been developed under a squared error loss function as well as under a LINEX loss function using priors of non-informative type for the parameters. It has been seen that the estimators obtained are not available in nice closed forms, although they can be easily evaluated for a given sample by using suitable numerical methods. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under squared error as well as under LINEX loss functions.
MSC:
| 62C10 | Bayesian problems; characterization of Bayes procedures |
| 62F10 | Point estimation |
| 62N01 | Censored data models |
| 62F15 | Bayesian inference |
| 65C60 | Computational problems in statistics (MSC2010) |
Keywords:
Bayes estimators; maximum likelihood estimator; non-informative-type priors; type I censoring; type II censoring; squared error loss function; LINEX loss functionReferences:
| [1] | Aitchison, L. J.; Dunsmore, I. R., Statistical Prediction Analysis (1975), Cambridge University Press: Cambridge University Press London · Zbl 0327.62043 |
| [2] | Cohen, A. C., Maximum likelihood estimation in the Weibull distribution based on complete and censored samples, Technometrics, 7, 579 (1965) |
| [3] | Cohen, A. C., Progressively censored samples in life testing, Technometrics, 5, 327-329 (1963) · Zbl 0124.35401 |
| [4] | Ferguson, T. S., Mathematical Statistics: A Decision Theoretic Approach (1967), Academic Press: Academic Press New York · Zbl 0153.47602 |
| [5] | Gupta, R. C.; Gupta, R. D.; Gupta, P. L., Modeling failure time data by Lehman alternatives, Comm. Statist. Theory Methods, 27, 4, 887-904 (1998) · Zbl 0900.62534 |
| [6] | Johnson, N. L.; Kotz, S.; Balakrishnan, N., Continuous Univariate Distributions, vol. 1 (1994), Wiley: Wiley New York · Zbl 0811.62001 |
| [7] | Khatree, R., Estimation of guarantee time and mean after warrantee for two-parameter exponential failure model, Aust. J. Statist., 34, 2, 207-215 (1992) · Zbl 0781.62150 |
| [8] | Lawless, J. F., Statistical Method for Life Time Data (1982), Wiley: Wiley New York · Zbl 0541.62081 |
| [9] | Parsian, A., On the admissibility of an estimator of a normal mean vector under a linex loss function, Ann. Inst. Statist. Math., 42, 657-669 (1990) · Zbl 0747.62012 |
| [10] | Shawky, A. I.; Abu-Zinadah, H. H., Exponentiated Pareto distribution: Different method of estimations, Int. J. Contemp. Math. Sci., 4, 14, 677-693 (2009) · Zbl 1186.62032 |
| [11] | Singh, U.; Gupta, P. K.; Upadhyay, S. K., Estimation of parameters for exponentiated Weibull family under type II censoring scheme, Comput. Statist. Data Anal., 48, 509-523 (2005) · Zbl 1429.62453 |
| [12] | Varian, H. R., A Bayesian approach to real estate assessment, (E. F., Stephen; A., Zellner, Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage (1975), North-Holland: North-Holland Amsterdam), 195-208 · Zbl 0365.62114 |
| [13] | Zellner, A., Bayesian estimation and prediction using asymmetric loss Function, J. Amer. Statist. Assoc., 81, 446-451 (1986) · Zbl 0603.62037 |
| [14] | Zellner, A.; Geisel, M. S., Sensitivity of control to uncertainty and form of the cotenant function, (G. W., Donald, The Future of Statistics (1968), Academic Press: Academic Press New York), 269-289 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
