Under some restriction, we establish the minimum volume confidence region for parameters of Pareto distribution, which can be applied to complete samples and, as well as left, right or doubly censored samples. It is not only computationally convenient, but also almost as accurate as the best confidence region in the literature, the computation of which is difficult in the double or left censoring case.
Critical value Double censoring Parameter Pivotal quantity Sufficient statistic
Mathematics Subject Classification
This is a preview of subscription content, log in to check access.
This research is partially supported by the National Natural Science Foundation of China (NSFC, Grant No. 11561073). The author would like to thank Editors and anonymous referees for valuable comments, corrections and suggestions.
Abdel-Ghaly AA, Attia AF, Ali HM (1998) Estimation of the parameters of Pareto distribution and the reliability function using accelerated life testing with censoring. Commun Stat Simul Comput 27:469–484MathSciNetCrossRefzbMATHGoogle Scholar
Arnold BC (1983) Pareto distributions. International Cooperative Publishing House, FairlandzbMATHGoogle Scholar
Beirlant J, Teugels JL, Vynckier P (1996) Practical analysis of extreme values. Leuven University Press, LeuvenzbMATHGoogle Scholar
Bickel PJ, Doksum KA (2001) Mathematical statistics: basic ideas and selected topics, vol I, 2nd edn. Prentice Hall, New JerseyzbMATHGoogle Scholar
Hong CW, Wu JW, Cheng CH (2008) Computational procedure of performance assessment of lifetime index of Pareto lifetime businesses based on confidence interval. Appl Soft Comput 8:698–705CrossRefGoogle Scholar
Howlader HA, Hossain A (2002) Bayesian survival estimation of Pareto distribution of the second kind based on failure-censored data. Comput Stat Data Anal 38:301–314MathSciNetCrossRefzbMATHGoogle Scholar
Pareto V (1897) Couts d’economie politique. Rouge and cie, Lausanne and ParisGoogle Scholar
Parsi S, Ganjali M, Sanjari Farsipour N (2010) Simultaneous confidence intervals for the parameters of Pareto distribution under progressive censoring. Commun Stat 39:94–106MathSciNetCrossRefzbMATHGoogle Scholar
R Core Team (2014) R: a Language and environment for statistical computing, R foundation for statistical computing, Vienna. http://www.R-project.org/
Reed WJ, Jorgensen M (2004) The double Pareto-lognormal distributiona new parametric model for size distributions. Commun Stat 33:1733–1753CrossRefzbMATHGoogle Scholar
Seal HL (1980) Survival probabilities based on Pareto claim distributions. Astin Bull 11:61–72CrossRefGoogle Scholar
Wu JW, Lee WC, Chen SC (2006) Computational comparison for weighted moments estimators and BLUE of the scale parameter of a Pareto distribution with known shape parameter under type II multiply censored sample. Appl Math Comput 181:1462–1470MathSciNetzbMATHGoogle Scholar
Wu JW, Lee WC, Chen SC (2007) Computational comparison of prediction future lifetime of electronic components with Pareto distribution based on multiply type II censored samples. Appl Math Comput 184:374–406MathSciNetzbMATHGoogle Scholar