Araştırma Makalesi
Yıl 2018,
Cilt: 47 Sayı: 1, 145 - 173, 01.02.2018
Öz
Motivated by Torabi and Hedesh (2012), we propose a gamma extended family of distributions with two extra generator parameters. We present some special models and study general mathematical properties like asymptotes and shapes, ordinary and incomplete moments, generating and quantile functions, probability weighted moments, mean deviations, Bonferroni and Lorenz curves, asymptotic distributions of the extreme values, Shannon entropy, Rényi entropy, reliability and order statistics. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is determined. We de fine a new regression model based on the logarithm of the roposed distribution. The usefulness of the new models is proved empirically in three applications to real data.
Anahtar Kelimeler
Estimation Gamma distribution Generated family Maximum likelihood Mean deviation Moment Quantile function
Kaynakça
- Aas, K., and I. Ha (2006). The Generalized Hyperbolic Skew Student's t-Distribution. Journal of Financial Econometrics, 4, 275-309.
- Alexander, C., Cordeiro, G.M., Ortega, E.M.M. and Sarabia, J.M. (2012). Generalized betagenerated distributions. Computational Statistics and Data Analysis, 56, 1880-1897.
- Cordeiro, G.M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, 883-898.
- Cordeiro, G.M. and Lemonte, A.J. (2011). The -Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling. Computational Statistics and Data Analysis, 55, 1445-1461.
- Cordeiro, G.M., Nadarajah, S. and Ortega, E.M.M. (2013). General results for the beta Weibull distribution. Journal of Statistical Computation and Simulation, 83, 1082-1114.
- Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31, 497-512.
- Famoye, F., Lee, C., Olumolade, O. (2005). The beta-Weibull distribution. Journal of Sta- tistical Theory and Applications, 4, 121-136.
- Gradshteyn, I.S. and Ryzhik, I.M. (2000). Table of Integrals, Series, and Products, sixth edition. Academic Press, San Diego.
- Gupta, R.D., Kundu, D. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41, 173-188.
- Hansen, B.E. (1994). Autoregressive conditional density estimation. International Economic Review, 35, 705-730.
- Johnson, N.L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions. Volume 1, 2nd edition. John Wiley and Sons, New York.
- Johnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions. Volume 2, 2nd edition. John Wiley and Sons, New York.
- Kakde, C.S and Shirke, D.T. (2006). On Exponentiated Lognormal distribution. Interna- tional Journal of Agricultural and Statistics Sciences, 2, 319-326.
- Leadbetter, M.R., Lindgren, G. and Rootzeén, H. (1987). Extremes and Related Properties of Random Sequences and Processes. New York: Springer.
- Lawless, J. F. (2003). Statistical models and methods for lifetime data.
- Mudholkar, G.S., Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-real data. IEEE Transaction on Reliability, 42, 299-302.
- Mudholkar, G.S., Srivastava, D.K., Kollia, G.D. (1996). A generalization of the Weibull distribution with application to the analysis of survival data. Journal of American Statistical Association, 91, 1575-1583.
- Nadarajah, S., Cordeiro, G.M., Ortega, E.M.M. (2015) The Zografos-Balakrishnan-G family of distributions: Mathematical properties and applications. Communications in Statistics - Theory and Methods, 44, 186-215.
- Nadarajah, S. (2005). The exponentiated Gumbel distribution with climate application. Environmetrics, 17, 13-23.
- Nadarajah, S., Gupta, A.K. (2007). The exponentiated gamma distribution with application to drought data. Calcutta Statistical Association Bulletin, 59, 29-54.
- Nadarajah, S., Kotz, S. (2006). The exponentiated type distributions. Acta Applicandae Mathematicae, 92, 97-111.
- Ortega, E.M.M., Cordeiro, G.M. and Hashimoto, E.M. (2011). A log-linear regression model for the beta-Weibull distribution. Communications in Statistics-Simulation and Computa- tion, 40, 1206-1235.
- Ortega, E.M.M., Cordeiro, G.M. and Kattan, M.W. (2012). The negative binomial-beta Weibull regression model to predict the cure of prostate cancer. Journal of Applied Statistics, 39, 1191-1210.
- Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I. (1986). Integrals and Series, volumes 1, 2 and 3. Gordon and Breach Science Publishers, Amsterdam.
- Ristic, M.M. and Balakrishnan, N. (2012). The gamma exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82, 1191-1206.
- Smith, R.L. and Naylor, J.C. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 36, 358-369.
- Torabi, H. and Hedesh, N.M. (2012). The gamma-uniform distribution and its applications. Kybernetika, 48, 16-30.
- Wright, E.M. (1935). The asymptotic expansion of the generalized hypergeometric function. Proceedings of the London Mathematical Society, 10, 286-293.
- Zografos, K. and Balakrishnan, N. (2009). On families of beta- and generalized gammagenerated distributions and associated inference. Statistical Methodology, 6, 344-362.
Yıl 2018,
Cilt: 47 Sayı: 1, 145 - 173, 01.02.2018
Öz
Kaynakça
- Aas, K., and I. Ha (2006). The Generalized Hyperbolic Skew Student's t-Distribution. Journal of Financial Econometrics, 4, 275-309.
- Alexander, C., Cordeiro, G.M., Ortega, E.M.M. and Sarabia, J.M. (2012). Generalized betagenerated distributions. Computational Statistics and Data Analysis, 56, 1880-1897.
- Cordeiro, G.M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, 883-898.
- Cordeiro, G.M. and Lemonte, A.J. (2011). The -Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling. Computational Statistics and Data Analysis, 55, 1445-1461.
- Cordeiro, G.M., Nadarajah, S. and Ortega, E.M.M. (2013). General results for the beta Weibull distribution. Journal of Statistical Computation and Simulation, 83, 1082-1114.
- Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31, 497-512.
- Famoye, F., Lee, C., Olumolade, O. (2005). The beta-Weibull distribution. Journal of Sta- tistical Theory and Applications, 4, 121-136.
- Gradshteyn, I.S. and Ryzhik, I.M. (2000). Table of Integrals, Series, and Products, sixth edition. Academic Press, San Diego.
- Gupta, R.D., Kundu, D. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41, 173-188.
- Hansen, B.E. (1994). Autoregressive conditional density estimation. International Economic Review, 35, 705-730.
- Johnson, N.L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions. Volume 1, 2nd edition. John Wiley and Sons, New York.
- Johnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions. Volume 2, 2nd edition. John Wiley and Sons, New York.
- Kakde, C.S and Shirke, D.T. (2006). On Exponentiated Lognormal distribution. Interna- tional Journal of Agricultural and Statistics Sciences, 2, 319-326.
- Leadbetter, M.R., Lindgren, G. and Rootzeén, H. (1987). Extremes and Related Properties of Random Sequences and Processes. New York: Springer.
- Lawless, J. F. (2003). Statistical models and methods for lifetime data.
- Mudholkar, G.S., Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-real data. IEEE Transaction on Reliability, 42, 299-302.
- Mudholkar, G.S., Srivastava, D.K., Kollia, G.D. (1996). A generalization of the Weibull distribution with application to the analysis of survival data. Journal of American Statistical Association, 91, 1575-1583.
- Nadarajah, S., Cordeiro, G.M., Ortega, E.M.M. (2015) The Zografos-Balakrishnan-G family of distributions: Mathematical properties and applications. Communications in Statistics - Theory and Methods, 44, 186-215.
- Nadarajah, S. (2005). The exponentiated Gumbel distribution with climate application. Environmetrics, 17, 13-23.
- Nadarajah, S., Gupta, A.K. (2007). The exponentiated gamma distribution with application to drought data. Calcutta Statistical Association Bulletin, 59, 29-54.
- Nadarajah, S., Kotz, S. (2006). The exponentiated type distributions. Acta Applicandae Mathematicae, 92, 97-111.
- Ortega, E.M.M., Cordeiro, G.M. and Hashimoto, E.M. (2011). A log-linear regression model for the beta-Weibull distribution. Communications in Statistics-Simulation and Computa- tion, 40, 1206-1235.
- Ortega, E.M.M., Cordeiro, G.M. and Kattan, M.W. (2012). The negative binomial-beta Weibull regression model to predict the cure of prostate cancer. Journal of Applied Statistics, 39, 1191-1210.
- Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I. (1986). Integrals and Series, volumes 1, 2 and 3. Gordon and Breach Science Publishers, Amsterdam.
- Ristic, M.M. and Balakrishnan, N. (2012). The gamma exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82, 1191-1206.
- Smith, R.L. and Naylor, J.C. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 36, 358-369.
- Torabi, H. and Hedesh, N.M. (2012). The gamma-uniform distribution and its applications. Kybernetika, 48, 16-30.
- Wright, E.M. (1935). The asymptotic expansion of the generalized hypergeometric function. Proceedings of the London Mathematical Society, 10, 286-293.
- Zografos, K. and Balakrishnan, N. (2009). On families of beta- and generalized gammagenerated distributions and associated inference. Statistical Methodology, 6, 344-362.
Toplam 29 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | İstatistik |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Şubat 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 47 Sayı: 1 |