He, Hui; Zhou, Na; Zhang, Ruiming On estimation for the Pareto distribution. (English) Zbl 1486.62061 Stat. Methodol. 21, 49-58 (2014). Summary: In this work, we obtain the \(r\)-th raw moments of the probability density function (PDF) and reliability function (RF) for the Pareto distribution under the maximum likelihood estimation (MLE) and uniform minimum variance unbiased estimation (UMVUE). We derive some large sample properties of the estimators, the MLE and UMVUE of the PDF as well as RF. Two examples are provided to compute the efficient estimations of PDF and RF numerically. Our results indicate that there are no absolute superiorities of MLEs over the UMVUEs of PDF and RF and vice versa. Cited in 2 Documents MSC: 62F10 Point estimation 62E15 Exact distribution theory in statistics Keywords:Pareto distribution; MLE; UMVUE; probability density function; reliability function Software:DLMF PDFBibTeX XMLCite \textit{H. He} et al., Stat. Methodol. 21, 49--58 (2014; Zbl 1486.62061) Full Text: DOI References: [1] Asrabadi, B. R., Estimation in the Pareto distribution, Metrika, 37, 199-205 (1990) · Zbl 0693.62032 [2] Dixit, U. J.; Jabbari Nooghabi, M., Efficient estimation in the Pareto distribution, Stat. Methodol., 7, 687-691 (2010) · Zbl 1232.62044 [3] Dyer, D., Structural probability bounds for the strong Pareto law, Canad. J. Statist., 9, 71-77 (1981) · Zbl 0484.62052 [4] Fahidy, T. Z., Applying Pareto distribution theory to electrolytic powder production, Electrochem. Commun., 13, 262-264 (2011) [5] Ijiri, Y.; Simon, H. A., Some distributions associated with Bose-Einstein statistics, Proc. Natl. Acad. Sci., 72, 1654-1657 (1975) [6] Olver, F. W.; Lozier, D. W.; Boisvert, R. F., NIST Handbook of Mathematical Functions (2010), Cambridge University Press: Cambridge University Press New York · Zbl 1198.00002 [7] Pareto, V., Cours d’Economie Politique (1964), Librairie Droz: Librairie Droz Geneva [8] Reed, W. J.; Jorgensen, M., The double Pareto-lognormal distribution—a new parametric model for size distributions, Comm. Statist. Theory Methods, 33, 1733-1753 (2004) · Zbl 1134.62313 [9] Seal, H. L., Survival probabilities based on Pareto claim distributions, Astin Bull., 11, 61-72 (1980) [10] Wong, R., Asymptotic Approximations of Integrals (1989), Academic Press: Academic Press Boston · Zbl 0679.41001 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.