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2011 | 12 | 1 | 97-114
Article title

The Beta Pareto Distribution

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
In this paper, we introduce a generalization—referred to as the beta Pareto distribution, generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of the beta Pareto distribution. We derive expressions for the kth moments of the distribution, variance, skewness, kurtosis, mean deviation about the mean, mean deviation about the median, Rényi entropy, Shannon entropy. We also discuss simulation issues, estimation of parameters by the methods of moments and maximum likelihood.
Year
Volume
12
Issue
1
Pages
97-114
Physical description
Contributors
  • Sana’a University
References
  • BROWN, B.W, SPEARS, F.M and LEVY, L.B. (2002): The log F: a distribution for all seasons. Comput. Statist., 17, 47–58.
  • EUGENE, N., LEE, C. and FAMOYE, F. (2002): Beta-normal distribution and its applications. Commun Statist—Theory Methods. 31, 497–512.
  • GUPTA, A.K. and NADARAJAH, S. (2004): On the moments of the beta normal distribution. Commun Statist—Theory Methods. 33, 1–13.
  • HINKLEY, D. (1978): Likelihood inference about location and scale parameters. Biometrika. 65(2), 253-261.
  • JENNINGS, D. (1986): Judging inference adequacy in logistic regression. JASA. 81(394), 471-476.
  • JONES, M. C. (2004): Families of distributions arising from distributions of order statistics. Test. 13, 1–43.
  • NADARAJAH, S. and KOTZ, S. (2004): The beta Gumbel distribution. Math Probab Eng. 10, 323–332.
  • RÉNYI, A. (1961): On measures of entropy and information. In: Proceedings of the fourth Berkeley symposium on mathematical statistics and probability. vol. 1. Berkeley: University of California Press. p. 547–61.
  • SONG, K. S. (2001): RÉNYI information, log likelihood and an intrinsic distribution measure. J Statisst Plan Inference. 93, 51–69.
  • SPROTT, D. (1980): Maximum likelihood in small samples: Estimation in the presence of a nuisance parameters. Biometrija. 67(3), 515-523.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-746d43ca-95d9-46ba-b134-b48d4380b055
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