The usefulness of the new models is proved empirically in three applications to real data.
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez:Motivated by Torabi and Hedesh (2012), we propose a gamma extended family of distributions with two extra generator parameters.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı:The usefulness of the new models is proved empirically in three applications to real data.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:2012 Verileri
⚙️Değişkenler:Estimation · Gamma distribution · Generated family
Abstract
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 define 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.
NADARAJAH, S., CORDEIRO, G. M., RAMİRES, T. G., ORTEGA, E. M. M. (2022). An alternative two-parameter gamma generated family of distributions: properties and applications. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 1, 145–173. https://ajindex.com/articles/529864
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. N