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Simplification of joint confidence regions for the parameters of the Pareto distribution

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Abstract

The Pareto distribution is an important distribution in statistics, which has been widely used in economics to model the distribution of incomes. Separate interval estimations for parameters of the Pareto distribution have been well established in the literature. For a type-II right censored sample, Chen (Metrika 44:191–197, 1996) proposed a joint confidence region for the parameters. Wu (Comput Stat Data Anal 52:3779–3788, 2008) derived a joint confidence region for any type-II censored sample, but its computation is difficult. Both Wu’s and Chen’s results are simplified in this paper, and some errors are corrected. The methodology used in this article can be applied to other distributions, as long as the underlying distribution can be transformed to the standard exponential distribution in a simple way.

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Acknowledgments

This research is partially supported by the Natural Science Foundation of China (NSFC, Grant No. 1161054). The author is very grateful to anonymous referees for careful readings and valuable comments, suggestions and corrections, which significantly improved the presentation of this article.

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  1. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, Yunnan, China

    Jin Zhang

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  1. Jin Zhang
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Correspondence to Jin Zhang.

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Zhang, J. Simplification of joint confidence regions for the parameters of the Pareto distribution. Comput Stat 28, 1453–1462 (2013). https://doi.org/10.1007/s00180-012-0354-9

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  • DOI: https://doi.org/10.1007/s00180-012-0354-9

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