Keywords:-

Keywords: Average Years of Schooling (AYS); Generalized Gamma Distribution; Generalized Gamma Regression; Berndt-Hall-Hall-Hausman (BHHH) algorithm; Maximum Likelihood Estimation (MLE).

Article Content:-

Abstract

A popular statistical tool that works particularly well in situations when the data distribution is positively skewed and asymmetrical is the generalized gamma (GG) distribution. In many real-world scenarios, multiple factors can influence different outcomes at the same time. The Generalized Gamma Regression (GGR) model, which is intended for answers that have a Generalized Gamma (GG) distribution, is presented in this article. The Berndt-Hall-Hall-Hausman (BHHH) algorithm is used to optimize the Maximum Likelihood Estimation (MLE) technique, which is used for parameter estimation in the GGR model. We employ the Maximum Likelihood Ratio Test (MLRT) and the Wald test for partial testing to evaluate the model's relevance. Thorough simulation validation shows that the GGR model is capable of accurately estimating parameters with little bias. To demonstrate its usefulness, we deployed the GGR model to a real-world case study. We specifically use it to examine the average years of schooling (AYS) in Central Java, Indonesia. In the final analysis, the current research emphasizes the advantages of applying the GGR model for generalized gamma distributed responses and demonstrates the model's resilience in parameter estimation.

References:-

References

Cepeda-Cuervo, E., Corrales, M., Cifuentes, M.V. and Zarate, H. 2016. On gamma regression residuals, Journal of the Iranian Statistical Society 15(1), 29–44 (2016).

Nasution, A.S., Purhadi and Sutikno. 2017. Estimasi Parameter dan Pengujian Hipotesis Pada Model Regresi Gamma (Studi Kasus: Pemodelan Pencemaran Sungai di Surabaya), Paidagogeo: Jurnal Pendidikan 2(2), 17–26.

Suyitno, S.: Penaksiran Parameter dan Pengujian Hipotesis Model Regresi Weibull Univariat, Jurnal Eksponensial 8(2), 179–183 (2017).

Zhang, Z. 2016. Parametric regression model for survival data: Weibull regression model as an example, Annals of Translational Medicine 4(24), 1–8.

Bednarski, T. and Skolimowska-Kulig, M. 2019. On scale Fisher consistency of maximum likelihood estimator for the exponential regression model under arbitrary frailty, Statistics and Probability Letters 150, 9–12.

Davidov, O. and Zelen, M. 2000. Exact tests for exponential regression, Journal of Statistical Planning and Inference 88(1), 87–97.

Palm, B.G., Bayer, F.M., Cintra, R.J., Pettersson, M.I. and Machado, R. 2019. Rayleigh Regression Model for Ground Type Detection in SAR Imagery, IEEE Geoscience and Remote Sensing Letters 16(10), 1660–1664.

Yasin, H., Inayati, S. and Setiawan. 2022. 3-Parameter Gamma Regression Model for Analyzing Human Development Index of Central Java Province, BAREKENG: Jurnal Ilmu Matematika dan Terapan 16(1), 171–180.

Diantini, N. L. S., Purhadi, and Choiruddin, A. 2023. Parameter estimation and hypothesis testing on three parameters log normal regression. In AIP Conference Proceedings (Vol. 2554, No. 1, p. 030024). AIP Publishing LLC.

Sanchez, R. and Mackenzie, S.A. 2016. Information thermodynamics of cytosine DNA methylation, PLoS ONE 11(3), 1–20.

Stacy, E.W. 1962. A Generalization of the Gamma Distribution, The Annals of Mathematical Statistics 33(3), 1187–1192.

Stacy, E.W. and Mihram, G. A. 1965. Parameter Estimation for a Generalized Gamma Distribution, Technometrics 7(3), 349–358.

Shanker, R. and Shukla, K.K. 2016. On modeling of lifetime data using three-parameter generalized lindley and generalized gamma distributions, Biom Biostat Int J. 4(7), 283–288.

Yasin, H., Purhadi and Choiruddin, A. 2022. Estimasi Parameter dan Pengujian Hipotesis Model Geographically Weighted Generalized Gamma Regression, Jurnal Gaussian 11(1), 140–152.

Berndt, E.K., Hall, B.H., Hall, R.E. dan Hausman, J.A. 1974. Estimation and Inference in Nonlinear Structural Models, Annals of Economic and Social Measurement, Vol. 3, No. 4, 653–665.

Magee, L. 1990. R2 Measures Based on Wald and Likelihood Ratio Joint Significance Tests, The American Statistician, Vol. 44, No. 3, 250–253. http://doi.org/10.2307/2685352.

Zhang, D. 2017. A Coefficient of Determination for Generalized Linear Models, The American Statistician, Vol. 71, No. 4, 310–316. http://doi.org/10.1080/00031305.2016.1256839.

Burnham, K.P. dan Anderson, D.R. 2002, Model Selection and Inference: A Practical Information-Theoretic Approach, 2nd Ed., Springer-Verlag, New York. http://doi.org/10.2307/3803117.

BPS-Statistics of Jawa Tengah Province, LNCS Homepage https://jateng.bps.go.id/, last accessed 2023/02/17.

Biu, E. O., Nwakuya, M. T., and Wonu, N. 2019. Detection of Non-Normality in Data Sets and Comparison between Different Normality Test. Asian Journal of Probability and Statistics, Vol. 5, No.4, ISSN: 2582-0230, 1-20.

Downloads

Citation Tools

How to Cite
Yasin, H., & ., S. (2025). Generalized Gamma Regression Model: Simulation Study and Its Application. International Journal Of Mathematics And Computer Research, 13(06), 5335-5341. https://doi.org/10.47191/ijmcr/v13i6.08