The exponentiated Gompertz (EGZ) distribution has been recently used in almost all areas of human endeavours, starting from modelling lifetime data to cancer treatment. Various applications and properties of the EGZ distribution are provided by Anis and De (2020). This paper explores the important properties of the EGZ distribution under Bayesian discipline using two informative priors: the Gamma Prior (GP) and the Inverse Levy Prior (ILP). This is done in the framework of five selected loss functions. The findings show that the two best loss functions are the Weighted Balance Loss Function (WBLF) and the Quadratic Loss Function (QLF). The usefulness of the model is illustrated by the use of reallife data in relation to simulated data. The empirical results of the comparison are presented through a graphical illustration of the posterior distributions.
exponentiated Gompertz distribution, loss functions, informative priors, Bayes estimators, posterior risks
Abu-Zinadah, Hanaa H. and Bakoban. R. A., (2017). "Bayesian estimation of exponentiated Gompertzdistribution under progressive censoring type-II." Journal of Computational and Theoretical Nanoscience, 14(11), pp. 5239–5247.
Ade, O. A., Olayode, F. and Bamidele, A., (2017). Performance rating of the exponentiated generalized Gompertz Makeham distribution: an analytical approach. American Journal of Theoretical and Applied Statistics, 6(5), pp. 228–235.
Alrajhi, S., Almarashi, A. M., Algarni, A. and Amein, M. M., (2020). Estimation for the generalized Gompertz distribution hybrid progressive censored samples. Journal of Intelligent & Fuzzy Systems, (Preprint), pp. 1–10.
Anis, M. Z., (2020). The Unit-Gompertz Distribution: Characterizations and Properties. arXiv preprint arXiv:2010.04347.
Anis, M. Z., De, D., (2020). Some more properties of the unit- Gompertzdistribution. arXiv preprint arXiv:2006.06439.
Bakouch, H. S., Bar, A. M. T. A. E. and Tanta, (2017). A new weighted Gompertzdistribution with applications to reliability data. Journal of Applications of Mathematics, 62(3), pp. 269–296.
Bassiouny, A. H. E., Damcese, M. E., Mustafa, A. and Eliwa, M. S., (2017). Exponentiated generalized Weibull-Gompertz distribution with application in survival analysis. Journal of Statistics Applications & Probability, An International Journal, 6(1), pp. 7–16.
Chaturvedi, A., Bhatti, M. I. and Kumar, K., (2000). Bayesian analysis of disturbances variance in the linear regression model under asymmetric loss functions. Applied Mathematics and Computation, 114(2-3), pp. 149–153.
Chaturvedi, A., Gupta, S. and Bhatti, M. I., (2012). Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances. Journal of Multivariate Analysis, 104(1), pp.140–158.
Cordeiro, G. M., Alizadeh, M., Nascimento, A. D. C. and Rasekhi, M., (2016). The exponentiated Gompertz generated family of distributions: properties and applications. Chilean Journal of Statistics, 7(2), pp. 29–50.
Damcese, M. A. E., Mustafa, A., Desouky, B. S. E. and Mustafa, M. E., (2015). The odd generalized exponential Gompertz distribution. Applied Mathematics, 6(14), pp. 2340–2353.
Dey, S., Moala, F. A. and Kumar, D., (2018). Statistical properties and different methods of estimation of Gompertz distribution with application. Journal of Statistics and Management Systems, 21(5), pp. 839–876.
Gohary, A. E., Alshamrani, A. and Otaibi, A. N. A., (2013). The generalized Gompertz distribution. Journal of Applied Mathematical Modelling, 37 (1), pp. 13–24.
Hoseinzadeh, Akram, Mohsen Maleki, Zahra Khodadadi and Javier E., (2019). Contreras-Reyes. The skew-reflected-Gompertz distribution for analyzing symmetric and asymmetric data. Journal of Computational and Applied Mathematics 349, pp. 132–141.
Ieren, T. G., Kromtit, F. M., Agbor, B. U., Eraikhuemen, I. B. and Koleoso, P. O. (2019). A power Gompertz distribution: model, properties and application to bladder cancer data. Asian Research Journal of Mathematics, 15(3), pp. 1–14.
Jafari, A. A., Tahmasebi, S. and Alizadeh, M., (2014). The Beta-Gompertz distribution. Revista Colombiana de Estadística, 37(1), pp. 139–156.
Jha, M. K., Dey, S., Alotaibi, R. M. and Tripathi, Y. M., (2020). Reliability estimation of a multicomponent stress-strength model for unit Gompertz distribution under progressive Type II censoring. Quality and Reliability Engineering International, 36(3), pp. 965–987.
Mazucheli, J., Menezes, A. F. and Dey, S., (2019). Unit-Gompertz distribution with applications. Statistica, 79(1), pp. 25–43.
Obeidat, M., Al-Nasser, A. and Al-Omari, A. I., (2020). Estimation of generalized Gompertz distribution parameters under ranked-set sampling. Journal of Probability and Statistics, pp. 1–14.
Saraçoglu, B., Asgharzadeh, A., Kazemi, M., Kinaci, I. and Akdam, N., (2014). Statistical inference for the generalized Gompertz distribution. Conference: 9-th International Statistics Day Symposium, Antalya, Turkey, pp. 1–10.
Sherpiency, E. A. E., Ibrahim, S. A. and Bedar, R. E., (2013). A new bivariate distribution with generalized Gompertz marginals. Asian Journal of Applied Sciences, 1(4), pp. 141–150.
Shrivastava, A., Chaturvedi, A. and Bhatti, M. I., (2019). Robust bayesian analysis of a multivariate dynamic model. Physica A: Statistical Mechanics and its Applications, pp. 528, 121451.
Zinadah, H. H. A., (2014). Bayesian Estimation on the exponentiated Gompertz distribution under Type II censoring. International Journal of Contemporary Mathematical Sciences, 9(11), pp. 497–505.
Zinadah, H. H. A., (2014). Goodness-of-fit tests for the exponentiated Gompertz distribution. International Journal of Innovation in Science and Mathematics, 2(4), pp. 2347–9051.
Zinadah, H. H. A., (2014a). Six methods of estimation for shape parameter of exponentiated Gompertz distribution. Applied Mathematical Sciences, 8(88), pp. 4349–4359.
Zinadah, H. H. A., OUFI, A. S. A., (2016). Different method estimations of the three parameters of exponentiated Gompertz distribution. Applied Mathematics & Information Sciences, An International Journal, 10(2), pp. 705–710.
Zinadah, H. H. A., Oufi, A. S. A., (2014). Some characterizations of the exponentiated Gompertz distribution. International Mathematical Forum, 9(30), pp. 1427–1439.