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

Yıl 2011, Cilt: 8 Sayı: 2, 45 - 54, 17.10.2011

Öz

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.

Kaynakça

  • 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.

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

Yıl 2011, Cilt: 8 Sayı: 2, 45 - 54, 17.10.2011

Öz

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.

Kaynakça

  • 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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular İstatistiksel Analiz
Bölüm Araştırma Makaleleri
Yazarlar

Özge Elmastaş Gültekin

İsmihan Bayramoğlu

Yayımlanma Tarihi 17 Ekim 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 8 Sayı: 2

Kaynak Göster

APA Elmastaş Gültekin, Ö., & Bayramoğlu, İ. (2011). İki Değişkenli Geometrik Dağılım ve Genelleştirilmesi, Bağımlılık Ölçüleri ve Dağılım Özellikleri. İstatistik Araştırma Dergisi, 8(2), 45-54.