Simulation and Analysis of Gamma Distribution in Assessing Delay Rate Completion of the Curriculum in Schools
Abstract
Completion of the curriculum on time is one of the important indicators of the success of the learning process. However, various factors such as material difficulty and external distractions often cause delays in curriculum completion. This study aims to model the delay in curriculum completion using Gamma distribution, with the research location at SMP Negeri 1 Melinting, East Lampung. Primary data is obtained from schools, while secondary data comes from related literature. This study uses Monte Carlo simulation based on Gamma distribution with the parameters of mean delay () and degree of variance (). The results showed an average delay of about 2.4 weeks, with the Gamma distribution matching the actual data based on the Kolmogorov-Smirnov test. These findings suggest that the Gamma distribution can be an effective prediction tool for modeling curriculum completion delays. Managerial recommendations include the preparation of flexible schedules and the use of simulation models for risk mitigation. This research contributes to education managers in designing better time and resource management strategiesCompletion of the curriculum on time is one of the important indicators of the success of the learning process. However, various factors such as material difficulty and external distractions often cause delays in curriculum completion. This study aims to model the delay in curriculum completion using Gamma distribution, with the research location at SMP Negeri 1 Melinting, East Lampung. Primary data is obtained from schools, while secondary data comes from related literature. This study uses Monte Carlo simulation based on Gamma distribution with the parameters of mean delay () and degree of variance (). The results showed an average delay of about 2.4 weeks, with the Gamma distribution matching the actual data based on the Kolmogorov-Smirnov test. These findings suggest that the Gamma distribution can be an effective prediction tool for modeling curriculum completion delays. Managerial recommendations include the preparation of flexible schedules and the use of simulation models for risk mitigation. This research contributes to education managers in designing better time and resource management strategies
References
Adams, T., & Peterson, R. (2019). The impact of curriculum difficulty on completion times in educational settings: A statistical approach. Journal of Educational Statistics, 44(2), 232-245. https://doi.org/10.1080/00220620.2019.1573229
Chen, W., & Lee, Y. (2021). Simulation-based analysis of curriculum completion time in secondary education using Gamma distribution. International Journal of Education and Statistics, 36(1), 59-73. https://doi.org/10.1007/jedu.2021.0125
Goh, J., & Tan, C. (2024). Using Gamma distribution for curriculum planning and completion predictions. Educational Research Journal, 47(4), 481-493. https://doi.org/10.1108/ERJ.2024.4321
Huang, X., Zhang, L., & Li, Q. (2020). Modeling curriculum completion time with statistical approaches: The role of external factors. Asian Journal of Education Research, 19(3), 87-101. https://doi.org/10.1016/j.ajer.2020.05.003
Johnson, P., & Tan, M. (2022). Assessing the impact of natural disasters on curriculum completion: A probabilistic approach. Journal of Educational Management and Development, 29(5), 45-58. https://doi.org/10.1080/je.2022.4564321
Jones, S. (2016). Using log-normal distribution to model curriculum completion time in secondary education. Educational Studies Journal, 12(1), 27-39. https://doi.org/10.1007/jedu.2016.0045
Ministry of Education and Culture. (2022). National Education Annual Report: Curriculum Evaluation and Completion Time. Indonesian Ministry of Education and Culture.
Liu, Q., & Zhang, H. (2022). Application of the Gamma distribution in predicting curriculum completion times at universities. Educational Technology and Development Journal, 33(2), 151-162. https://doi.org/10.1007/jedu.2022.03.015
Miller, R., Davis, K., & Lee, J. (2023). The effects of unexpected disruptions on curriculum completion in online education environments. Journal of Educational Technology, 15(3), 123-138. https://doi.org/10.1080/jedtech.2023.1234597
Nguyen, H., Nguyen, M., & Hoang, D. (2020). Exploring the variability in curriculum completion times at high schools: A statistical model. Journal of Education Studies, 42(1), 69-84. https://doi.org/10.1016/j.jedu.2020.01.002
Nugroho, A., & Santoso, B. (2021). Application of Gamma Distribution to Model Academic Task Completion Time in Secondary School. Journal of Statistics and Education, 14(2), 145–155.
Putri, R., Wijaya, D., & Lestari, F. (2020). Analysis of the delay time of educational projects using gamma distribution. Journal of Education and Evaluation, 18(3), 231–240.
Rahman, A., & Dewi, L. (2020). Weibull Distribution App to Model the Delay of College-Level Education Projects. Journal of Applied Statistics, 12(1), 45–53.
Smith, J., Brown, R., & Martin, K. (2018). Predicting curriculum completion times using statistical models: A review. Journal of Curriculum Planning, 12(4), 230-245. https://doi.org/10.1007/jedu.2018.0143
Taylor, C., & Johnson, S. (2021). Modeling the influence of external disruptions on school curriculum completion. Journal of Educational Simulation, 34(2), 102-114. https://doi.org/10.1080/edsim.2021.12.1208
Wang, L. (2019). Predicting curriculum completion delays using statistical models: A comparison of Poisson and Gamma distributions. Journal of Educational Research, 38(4), 198-211. https://doi.org/10.1080/0022062X.2019.1604325
