A New Bivariate Distribution with Generalized Gompertz Marginals

Authors

  • E. A. El-Sherpieny Prof. of Mathematical Statistics, ISSR, Cairo University, Giza
  • S. A. Ibrahim Assist. Prof. of Mathematical Statistics, ISSR, Cairo University, Giza
  • Radwan E. Bedar Ph. D. Student of Mathematical Statistics, ISSR, Cairo University, Giza

Keywords:

Generalized Gompertz distribution, Maximum likelihood estimators, Moment estimators, Fisher information matrix

Abstract

In this paper, we introduce a new bivariate generalized Gompertz distribution, it is of Marshall-Olkin type. Some properties of the distribution are studied, as bivariate moment generating function, marginal moment generating function and conditional distribution. Parameters estimators using the maximum likelihood method are obtained. A numerical illustration is used to obtain maximum likelihood estimators (MLEs) and we study the behavior of the estimators numerically.

References

Block, H. and Basu, A. P. "A continuous bivariate exponential extension". Journal of American Statistical Association, vol. 69, 1031-1037, 1974.

Csorgo, S. and Welsh, A.H. "Testing for exponential and Marshall-Olkin distribution". Journal of Statistical Planning and Inference, vol. 23, 287-300, 1989.

El-Gohary, A., Alshamrani, A., Al-Otaibi, A. N. "The Generalized Gompertz Distribution". Applied Mathematical Modelling, vol. 37, issues 1-2, 13-24, 2013.

Kundu, D. and Gupta, R. D. "Bivariate generalized exponential distribution". Journal of Multivariate Analysis, vol. 100, no. 4, 581-593, 2009.

Mudholkar, G.S., Sirvastava, D.K., Freimer, M. "The exponentiated Weibull family: a reanalysis of the bus motor failure data". Technometrics. 37, 436-445, 1995.

Marshall, A. W. and Olkin, I. A. "A multivariate exponential distribution". Journal of the American Statistical Association. 62, 30-44, 1967.

Sarhan, A. and Balakrishnan, N. "A new class of bivariate distributions and its mixture". Journal of the Multivariate Analysis. 98 1508-1527, 2007.

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Published

2013-10-20

How to Cite

El-Sherpieny, E. A., Ibrahim, S. A., & Bedar, R. E. (2013). A New Bivariate Distribution with Generalized Gompertz Marginals. Asian Journal of Applied Sciences, 1(4). Retrieved from https://www.ajouronline.com/index.php/AJAS/article/view/520

Issue

Vol. 1 No. 4 (2013): October 2013

Section

Articles

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