İki Değişkenli Geometrik Dağılım ve Genelleştirilmesi, Bağımlılık Ölçüleri ve Dağılım Özellikleri

Year 2011, Volume: 8 Issue: 2, 45 - 54, 17.10.2011

Özge Elmastaş Gültekin İsmihan Bayramoğlu

Abstract

Bu çalışmada, Marshall ve Olkin’in iki değişkenli geometrik dağılımına ilişkin dağılım özellikleri araştırılmış ve uyumluluk ölçüsü Kendall Tau elde edilmiştir. Aynı zamanda, iki değişkenli geometrik dağılımın En Çok Olabilirlik tahmin edicisi elde edilmiş ve çok değişkenli duruma genelleştirilmesi verilmiştir.

Keywords

Bernoulli Dağılımı, Bernoulli Marjinali, En Çok Olabilirlik, Geometrik Dağılım, Uyumluluk Ölçüsü, Yaşam Fonksiyonu

Bivariate Geometric Distribution and Its Generalizations, Dependence Measures and the Distribution Properties

Abstract

In this study, the distribution properties of Marshall and Olkin’s bivariate geometric distribution are studied and the concordance measure Kendall’s Tau is obtained. Also, Maximum Likelihood estimators of the bivariate geometric distribution are obtained and generalization to multivariate case is given.

Keywords

Bernoulli Distribution, Bernoulli Marginals, Maximum Likelihood, Geometric Distribution, Concordance Measure, Survival Function

References

• Asha, G., Sankaran, P. G., Unnikrishnan N. N., 2003. Probability Models With Constant Total Failure Rate. Communications in Statistics-Theory and Methods, 32(6), 1089-1099.
• Azlarov, T. A., Volodin, N. A., 1982. On The Discrete Analog Of Marshall-Olkin's Distribution. Stability problems for Stochastic Models. Lecture Notes in Mathematics, 982, Spinger, Berlin-New York, 17-23.
• Cox, D. R., 1972. Regression Models And Life-Tables. J. Roy. Statist. Soc. Ser. B, 34, 187-220.
• Dhar, S. K., 1998a. Data Analysis With Discrete Analogue Of Freund’s Model. J. Appl. Statist. Sci., 7, 169-183.
• Dhar, S. K., 1998b. Modeling With A Bivariate Geometric Distribution. Advances On Methodological And Applied Aspects Of Probability And Statistics. Edited by N. Balakrishnan, Gordon and Breach Science Publishers, IISA 98 McMaster Conference Proceedings, 1, 101-109.
• Dhar, S. K., Balaji, S., 2006. On The Characterization Of A Bivariate Geometric Distribution. Communications in Statistics-Theory and Methods, 35, 759-765.
• Hawkes, A. G., 1972. A Bivariate Exponential Distribution With Applications To Reliability. Journal of the Royal Statistical Society, Ser. B, 34, 129-131.
• Krishna, H., Pundir, S. P., 2009. A Bivariate Geometric Distribution With Applications To Reliability. Communications in Statistics-Theory and Methods, 38, 1079-1093.
• Marshall, A. W., Olkin, I., 1985. A Family Of Bivariate Distributions Generated By The Bernoulli Distribution. J. Am. Stat. Assoc., 80, 332-338.
• Mitov, K., Nadarajah, S., 2005. Limit Distributions For The Bivariate Geometric Maxima. Extremes, 8, 357-370.
• Nadarajah, S., 2008. Marshall And Olkin's Distributions. Acta. Appl. Math., 103, 87-100.
• Nair, K. R. M., Nair, N. U., 1988. On Characterizing A Bivariate Geometric Distribution. Journal of the Indian Statistical Association, 26, 45-49.
• Nelsen, B. R., 1999. An Introduction To Copulas. Springer, New york.
• Phatak, A. G., Sreehari, M., 1981. Some Characterizations of A Bivariate Geometric Distribution. J. Ind. Statist. Assoc., 19, 141-146.
• Roy, D., 1993. Reliability Measures In The Discrete Bivariate Set-Up And Related Characterization Results For A Bivariate Geometric Distribution. Journal of Multivariate Analysis, 46, 362-373.