A Simulation Study on The Simulated Annealing Algorithm in Estimating The Parameters of Generalized Gamma Distribution
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Keywords:
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Simulated Annealing Algorithm, Generalized Gamma Distribution, Parameters Estimation Methods, Log-Likelihood Function
Abstract
The gamma distribution is one of the most widely used statistical distribution in fitting various real life data set in the field of the reliability to fit failure data, because it is sufficiently flexible to deal with decreasing, constant, and increasing failure rates. In this article, the stock investment valuation model has been presented on the assumption of Gamma distribution. The purpose is to analysis profitability of investment in the property development sector in Malaysia based on the investment rate of return on investment. The flow of the investment cash and the accumulation of the share units over the investment period have been presented. it demonstrated the computing of MIRR by the case of a company which experienceed distributing a treasury share dividend, which increases the small portion of investor’s share units instead of receiving the dividend in cash. As the MIRR might exhibit negative values, the Gamma distribution of the transformed MIRR for certain investment periods is developed and the method of moment is applied to estimate the parameters. The study revealed that the transformed MIRR is well fitted with Gamma distribution for four years to eight years investment periods. It is shown that this approach has a better performance return on investment in Malaysia property sector from 2008 to 2018.
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Pradhan, B. and D. Kundu (2011). Bayes Estimation and Pre- diction of The Two-Parameter Gamma Distribution. Journal of Statistical Computation and Simulation, 81(9); 1187–1198
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Stacy, E. W. (1962). A Generalization of The Gamma Distribu- tion. The Annals of Mathematical Statistics, 33(3); 1187–1192
Tang, L. C. and W. T. Cheong (2004). Cumulative Confor-
mance Count Chart with Sequentially Updated Parameters.
Institute of Industrial Engineers Transactions, 36(9); 841–853
Yonar, A. Ş. and N. P. Yapici (2020). A Novel Differential Evolution Algorithm Approach for Estimating The Parame- ters of Gamma Distribution: An Application to The Failure Stresses of Single Carbon Fibres. Hacettepe Journal of Mathe-
matics and Statistics; 1–22
Zhao, W., J. Li, X. Yang, Q. Peng, and J. Wang (2018). Inno-
vative CFAR Detector with Effective Parameter Estimation Method for Generalised Gamma Distribution and Iterative Sliding Window Strategy. IET Image Processing, 12(1); 60– 69
Abubakar, H. and S. R. M. Sabri (2021a). Incorporating Sim- ulated Annealing Algorithm in The Weibull Distribution for Valuation of Investment Return of Malaysian Property Development Sector. International Journal for Simulation and Multidisciplinary Design Optimization, 12; 22
Abubakar, H. and S. R. M. Sabri (2021b). A Simulation Study on Modified Weibull Distribution for Modelling of Invest-
ment Return. Pertanika Journal of Science and Technology,
29(4)
Agarwal, S. K. and J. A. Al-Saleh (2001). Generalized Gamma
Type Distribution and its Hazard Rate Function. Communi-
cations in Statistics-Theory and Methods, 30(2); 309–318
Amoroso, L. (1925). Ricerche Intorno Alla Curva Dei Redditi.
Annali Di Matematica Pura Ed Applicata, 2(1); 123–159
Balakrishnan, N. and Y. Peng (2006). Generalized Gamma
Frailty Model. Statistics in Medicine, 25(16); 2797–2816
Bertsimas, D. and J. Tsitsiklis (1993). Simulated Annealing.
Statistical Science, 8(1); 10–15
Chen, L., V. P. Singh, and F. Xiong (2017). An Entropy-Based
Generalized Gamma Distribution for Flood Frequency Anal-
ysis. Entropy, 19(6); 239
Crama, Y. and M. Schyns (2003). Simulated Annealing for
Complex Portfolio Selection Problems. European Journal of
Operational Research, 150(3); 546–571
Dey, S., E. Garboczi, and A. M Hassan (2021). Method of
Moment Analysis of Carbon Nanotubes Embedded in a Lossy Dielectric Slab Using a Multilayer Dyadic Green’s Function. TechRxiv
Du, K. L. and M. Swamy (2016). Simulated Annealing. In Search and Optimization by Metaheuristics. Springer; 29–36
Eric, U., O. M. O. Olusola, and F. C. Eze (2020). A Study of Properties and Applications of Gamma Distribution. Statis- tics, 4(2); 52–65
Franses, P. H. (2016). A Note on The Mean Absolute Scaled Error. International Journal of Forecasting, 32(1); 20–22
Franzin, A. and T. Stützle (2019). Revisiting Simulated Anneal- ing: A Component-Based Analysis. Computers and Operations Research, 104; 191–206
Frías-Paredes, L., F. Mallor, M. Gastón-Romeo, and T. León (2018). Dynamic Mean Absolute Error as New Measure for Assessing Forecasting Errors. Energy Conversion and Manage- ment, 162; 176–188
Hirose, H. (1995). Maximum Likelihood Parameter Estima- tion in The Three-Parameter Gamma Distribution. Compu- tational Statistics and Data Analysis, 20(4); 343–354
Johnson, N. L., S. Kotz, and N. Balakrishnan (1995). Continu- ous Univariate Distributions Volume 2. John wiley & sons
Khodabina, M. and A. Ahmadabadib (2010). Some Properties of Generalized Gamma Distribution. Mathematical Sciences Lawless, J. (2003). Statistical Models and Methods for Lifetime
Data.
Hoboken, New Jersey: A John Wiley and Sons. Inc Mead, M., M. M. Nassar, and S. Dey (2018). A Generalization of Generalized Gamma Distributions. Pakistan Journal of
Statistics and Operation Research; 121–138
Mudholkar, G. S. and D. K. Srivastava (1993). Exponentiated
Weibull Family for Analyzing Bathtub Failure-Rate Data.
Institute of Electrical and Electronics Engineers Transactions on
Reliability, 42(2); 299–302
Nadarajah, S. and A. K. Gupta (2007). The Exponentiated
Gamma Distribution with Application to Drought Data. Cal-
cutta Statistical Association Bulletin, 59(1-2); 29–54
Nagatsuka, H. and N. Balakrishnan (2012). Parameter andQuantile Estimation for The Three-Parameter Gamma Dis- tribution Based on Statistics Invariant to Unknown Location. Journal of Statistical Planning and Inference, 142(7); 2087– 2102
Ortega, E. M., G. M. Cordeiro, M. A. Pascoa, and E. V. Couto (2012). The Log-Exponentiated Generalized Gamma Re- gression Model for Censored Data. Journal of Statistical Computation and Simulation, 82(8); 1169–1189
Orús, R., S. Mugel, and E. Lizaso (2019). Forecasting Financial Crashes with Quantum Computing. Physical Review A, 99(6); 060301
Peng, L. and Q. Yao (2003). Least Absolute Deviations Esti- mation for ARCH and GARCH Models. Biometrika, 90(4); 967–975
Pradhan, B. and D. Kundu (2011). Bayes Estimation and Pre- diction of The Two-Parameter Gamma Distribution. Journal of Statistical Computation and Simulation, 81(9); 1187–1198
Sabri, S. R. M. and W. M. Sarsour (2019). Modelling on Stock Investment Valuation for Long-Term Strategy. Journal of Investment and Management, 8(3); 60–66
Sayed, A. and S. Sabri (2022). Transformed Modified Internal Rate of Return on Gamma Distribution for Long Term Stock Investment. Journal of management Information and Decision Sciences, 25(S2); 1–17
Stacy, E. W. (1962). A Generalization of The Gamma Distribu- tion. The Annals of Mathematical Statistics, 33(3); 1187–1192
Tang, L. C. and W. T. Cheong (2004). Cumulative Confor-
mance Count Chart with Sequentially Updated Parameters.
Institute of Industrial Engineers Transactions, 36(9); 841–853
Yonar, A. Ş. and N. P. Yapici (2020). A Novel Differential Evolution Algorithm Approach for Estimating The Parame- ters of Gamma Distribution: An Application to The Failure Stresses of Single Carbon Fibres. Hacettepe Journal of Mathe-
matics and Statistics; 1–22
Zhao, W., J. Li, X. Yang, Q. Peng, and J. Wang (2018). Inno-
vative CFAR Detector with Effective Parameter Estimation Method for Generalised Gamma Distribution and Iterative Sliding Window Strategy. IET Image Processing, 12(1); 60– 69
Authors
Idris, A. A. ., & Shamsul Rijal Muhammad, S. (2022). A Simulation Study on The Simulated Annealing Algorithm in Estimating The Parameters of Generalized Gamma Distribution. Science and Technology Indonesia, 7(1), 84–90. https://doi.org/10.26554/sti.2022.7.1.84-90
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