Gompertz-G Family Generalized Lomax Distribution: Theory and Application
Abstract
In this study, a new, more flexible and fitting distribution is proposed by incorporating the Lomax distribution into the Gompertz-G family. Several important statistical properties of this new distribution, including the cumulative distribution function, the probability density function, the survival function, the hazard function, as well as the first and second moments, and other statistics. The model parameters were estimated using two methods: Maximum Likelihood Estimation (MLE) and Maximum Product Space Estimation (MPS). The performance of these two methods was compared through an extensive simulation study, regardless of the sample size and parameters, such as MSE and bias. The proposed distribution's efficiency was then evaluated using several real-world datasets. The fit indices of the proposed distribution were studied and compared with other standard distribution models, using goodness-of-fit AIC, BIC, CAIC, and HQIC. Eventually, several conclusions were presented for the findings obtained from the theoretical and applied parts.
References
[1] A. W. Marshall and I. Olkin, “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families,” Biometrika 92(2), 505–505 (2005).
[2] S. K. Althebhawi, A. Al-Haboobi, S. F. Altalaqani, Z. Al-hchimy, and A. AL-Adilee, “Transformation of Rayleigh distribution, properties, and application,” BIO Web Conf. 97, 00116 (2024).
[3] A. AL-Adilee, H. A. AL-Challabi, H. Falah, and D. S. Abdul-Zahra, “Generalized Lindley distribution using proportional hazard family and inference of failure time data,” Nonlinear Funct. Anal. Appl. 28(3), 793–800 (2023).
[4] H. S. M. Shibeeb, S. Altalaqani, and A. AL-Adilee, “A new version of Gumbel distribution using sine technique family: Properties, parameter estimation, and data analysis and comparison with fuzzy data,” Int. J. Neutrosophic Sci. 23(3) (2024).
[5] Akaike, H. (1978). A new look at the statistical model identification. Automatica, 19(6), 465–471.
[6] Radhi, A. R., Abdul Redhaa, Z., Neamah, I. A. (2021). A new modification of Kalman filter algorithm. International Journal of Nonlinear Analysis and Applications, 12(2), 1199–1212.
[7] Al-Khashab, A. A., Al-Haboobi, A., Al-Muslimawi, A. H. (2026). Computational investigation of non-Newtonian inelastic flows in a 4: 1 contraction based on artificial compressibility method. Results in Control and Optimization, 23,100730.
[8] Al-Haboobi, A., & Al-Muslimawi, A. H. (2025). Simulation of Newtonian Axisymmetric Thermal Channel Flow by Using a Developed Taylor–Galerkin/Pressure Correction Method. International Journal of Applied and Computational Mathematics, 11(5), 172.
[9] Al-Zaidi, Samah H. and Al-Haboobi, Anas,Investigation of inelastic power-law model under thermal conditions by using a developed method.(2025), Boletim da Sociedade Paranaense de Matematica, 43(1), 1–11. https://doi.org/10.5269/bspm.77563
[10] Lomax, K. S. (1954). Business failures: Another example of the analysis of failure data. Journal of the American statistical association, 49(268), 847–852.
[11] Alzaatreh, A., Lee, C., & Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71(1), 63–79.
[12] Cordeiro, G. M., Ortega, E. M. M., & Nadarajah, S. (2010). The exponentiated generalized class of distributions. Journal of Statistical Planning and Inference, 140(2), 375–401.
[13] Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883–898
[14] M. Alizadeh, G. M. Cordeiro, L. G. B. Pinho, and I. Ghosh, “The Gompertz-G family of distributions,” J. Stat. Theory Pract. 11, 179–207 (2017).
[15] M. W. A. Ramos, P. R. D. Marinho, R. V. da Silva, and G. M. Cordeiro, “The exponentiated Lomax Poisson distribution with an application to lifetime data,” Adv. Appl. Stat. 34(2), 107 (2013).
[16] Gupta, R. C., Ghitany, M. E., & Al-Mutairi, D. K. (2010). Estimation of reliability from Marshall–Olkin extended Lomax distributions. Journal of Statistical Computation and Simulation, 80(8), 937–947.
[17] Murthy, D. P., Xie, M., & Jiang, R. (2004). Weibull models. John Wiley & Sons.
[18] Cover, T. M. (1999). Elements of information theory. John Wiley & Sons.
[19] David, H. A., & Nagaraja, H. N. (2004). Order statistics. John Wiley & Sons
[20] B. Ranneby, “The maximum spacing method: An estimation method related to the maximum likelihood method,”Scand. J. Stat. 11, 93–112 (1984).
[21] Radhakrishna Rao, C., & Toutenburg, H. (1999). Linear models. Linear Models: Least Squares and Alternatives, 5–21.
[22] R. Cheng and N. Amin, “Maximum product of spacings estimation with application to the lognormal distribution,” Mathematical Report 79-1, University of Wales, IST, Cardiff (1979).
[23] Arnold, B. C., Balakrishnan, N., & Nagaraja, H. N. (2008). A first course in order statistics. Society for Industrial and Applied Mathematics.
[24] Cordeiro, G. M., Ortega, E. M., & Popović, B. V. (2015). The gamma-Lomax distribution. Journal of Statistical computation and Simulation, 85(2), 305.
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