The Log-Gamma-Pareto Distribution

Authors

  • Samir Kamel Ashour
  • Darwish Rashwan Said
  • Mahmoud abu agwa Fahim

Keywords:

Log-gamma-generated distributions, Pareto distribution, moments, order statistics, entropies.

Abstract

We study the log-gamma-Pareto distribution which includes as special cases two models such as gamma-Pareto and Pareto distributions. We demonstrate that its density function is an infinite linear combination of Pareto densities. Some mathematical properties of the new distribution are derived, such as moments, distribution of the order statistics, Shannon and Renyi entropies and maximum entropy characterization. We use maximum likelihood estimation to estimate model parameters and an application to a real data set illustrates its potentiality. We generate random numbers from the cdf of the distribution and obtain the mean, bias, mean square error, standard error, Kurtosis and Skewness for each parameter.

References

M. Amini, S. M. T. K. Mirmostafaeeand J. Ahmadi. "Log-gamma- generated families of distributions."A journal of Theoretical and Applied Statistics,Vol. 1, 2012.

U. J. Dixit and M. J. Nooghabi. "Efficient estimation in the Pareto distribution."Statistical Methodology, Vol. 7, 2010.

K. Zografosand N. Balakrishnan."On families of beta and generalized gamma-generated distributions and associated inference."Statistical Methodology, Vol. 6, 2009.

L. G. B. Pinho, G. M. Cordeiro and J. S. Nobre."The gamma-exponentiatedWeibull distribution."Journal of Statistical Theory and Applications,Vol. 11, 2012.

I. S. Gradshteynand I. M. Ryzhik. Table of integrals, series, and products.Acdemic Press, San Deigo, 2000.

M. M. Risticand N. Balakrishnan."The gamma-exponentiated exponential distribution."Journal of Statistical Computation and Simulation, Vol. 82, 2011.

C. E. Shannon."A mathematical theory of communication."The Bell System Technical Journal,Vol. 27, 1948.

A. Renyi."On measures of entropy and information," In: Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, I. University of California Press, Berkeley, 1961.

E. T. Jaynes. "Information theory and statistical mechanics."Physical Review, Vol. 106, 1957.

S. Nadarajah and M. Pal. "Explicit expressions for moments of gamma order statistics." Bulletin of the Brazilian Mathematical Society, Vol. 39, 2008.

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Published

2014-11-13

How to Cite

Ashour, S. K., Said, D. R., & Fahim, M. abu agwa. (2014). The Log-Gamma-Pareto Distribution. International Journal of Sciences: Basic and Applied Research (IJSBAR), 16(2), 357–374. Retrieved from https://gssrr.org/index.php/JournalOfBasicAndApplied/article/view/3038

Issue

Vol. 16 No. 2 (2014)

Section

Articles

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