Keywords:-
Keywords:
Exchange Rate, micture distribution, Log-Normal, Gamma, Weibull
Article Content:-
Abstract
As a world superpower, the United States has a very stable exchange rate and has a big impact on the currencies of other countries, like Indonesia. Probability modeling is therefore essential for analyzing the change in exchange rates between the Indonesian rupiah (IDR) and the US dollar (USD). In addition to comparing the distributions of two parameters, this study also discusses the use of several mixture 2 and 3 component distribution probability models, such as mixture 2 log-normal (ML2), mixture 2 Gamma (MG2), mixture 2 Weibull (MW2), mixture 3 Log-Normal (ML3), mixture 3 Gamma (MG3), and a mixture 3 Weibull (MW3). The maximum likelihood method is used for parameter estimation, and numerical methods like Akaike Information Cretarius (AIC) and Bayesian Information Cretarius (BIC) are used to select the best model, also known as the Goodness of Fit (GOF). Then, the GOF between the model distribution and the theoretical data is evaluated. The ML3 distribution-based daily USD/IDR exchange rate data can be best modeled using the MLE approach, as demonstrated by the results. We are able to reasonably forecast the risks associated with daily exchanges in the future on the basis of the identified models
References:-
References
1. Pangetuti, D. C., Fadila, A, and Nugraheni, S. 2022. Rupiah Exchange Rate Fluctuations in The US Dollar Purchasing Power Parity Theory and Fisher Effect Theory Testing, Nominal Barometer Riset Akuntansi dan Manajemen, 11 (1), 57-69
2. Pangestuti, D. C., and Tindangen, A. M. L. 2020. The Influence of Internal and External Factors on Firm Value. European Journal of Business and Management Research, 5(5).
3. Lin, C. S., Chiu, S. H., and Lin, T. Y. 2012. Empirical mode decomposition-based least squares support vector regression for foreign exchange rate forecasting. Econ. Model. 29, 2583–2590.
4. Huang, S. C., Chuang, P. J., and Wu, C. F. 2010. Chaos-based support vector regressions for exchange rate forecasting. Expert Syst. Appl. 37 (12), 8590–8598.
5. Dinger, Y., Li, S., and Li, L. 2009. An analysis on chaos behavior of currency exchange rate undulation. First International Workshop on Education Technology and Computer Science, Wuhan, Hubei, pp. 599–602.
6. Gradojevic, N., and Yang, J. 2006. Non-linear, non-parametric, non-fundamental exchange rate forecasting. J. Forecast. No. 25, 227–245.
7. Ridhwan, A., Kamel, M., Dahab, M. Y., and Hassanien, A., 2015. Forecasting exchange rates: a chaos-based regression approach. Int. J. Rough Sets Data Analysis 2 (1), 38–57
8. Chang P. H. K, and Melick, W. R. 1999. Workshop on Estimating and Interpreting Probability Density Functions. Bank for International Settlements Informations, Press Library Serv, 1 – 10.
9. Gurrola, P. 2008. Capturing fat-tail risk in exchange rate returns using SU curves: A comparison with the normal mixture and skewed Student distributions. J. Risk, 10, 73–100
10. Phoong, S. Y. and Phoong, S. W. 2022. A clustering analysis using finite mixture model. International Journal of Social Science Research, 4(2), 71-78.
11. Aitkin, M. and Rubin,D.B. 1985. Estimation and hypothesis terting in finite mixture models. Journal of the Royal Statistical Society B 47, 67-75
12. Atkinson,S. E. 1992. The performance of standard and hybrid EM algorithms for ML Estimation of the normal mixture model with censoring. Journal of Statistical Computation and Simulation 44, 105-115.
13. Atwood, L. D., Wilson, A. F., Bailey-Wilson, J. E., Carruth, J. N., and Elston, R. C. 1996. On the Distribution of likelihood ratio test statistic for a mixture of two normal distributions. Communications in Statistics-Simulation and Computation 25, 733-740.
14. Barndorff-Nielsen, O. 1965. Identifiability of mixture of exponential families. Journal of Mathematical Analysis and Applications 12, 115-121.
15. Basford, K. E. and McLachlan, G. J. 1985. Likelihood estimation for normal mixture models. Applied Statistics 34, 282-289.
16. Behboodian, J. 1970. On a mixture of normal distribution. Biometrika 57, 215-217.
17. Berdai, A. and Garel, B. 1996. Detecting a univariate normal mixture with two components. Statistics and Decisions. 16, 35-51.
18. Bezdek, J. C., Hathaway, R. M., and Huggins, V. J. 1985. Parametric estimation for normal mixture. Pattern Recognition 3, 79-84.
19. Blum, J. R. and Susarla, V. 1977. Estimation of a mixing distribution function. Annals of Probability 5, 200-209.
20. Brooks, S. P., Morgan, B. J. T., Ridout, M. S., and Pack, S. E. 1998. Finite mixture models for proportion. Biometrics 53, 1097-1115.
21. Campbell, N. A. 1984. Mixture models and atypical values. Mathematical Geology 16, 465-477.
22. Celeux, G. and Govaert, G. 1993. Comparison of the mixture and the classification maximum likelihood in cluster analysis. Journal of Statistical Computation and Simulation 47, 127-146.
23. Chandra, S. 1977. On the mixtures of probability distributions. Scandinavian Journal of Statistics: Theory and Applications 39, 105-112.
24. Choi, K. 1969. Estimators for the parameters of a finite mixture of distributions. Annals of the Institute of Statistical Mathematics 21, 107-116.
25. Day, N. E. 1969. Estimating the components of a mixture of two normal distributions. Biometrika 56, 463-474.
26. Delignette-Muller M. L, and Dutang, C. 2015. fitdistrplus: an R package for fitting distributions. J Stat Softw 64(4):1–34.
2. Pangestuti, D. C., and Tindangen, A. M. L. 2020. The Influence of Internal and External Factors on Firm Value. European Journal of Business and Management Research, 5(5).
3. Lin, C. S., Chiu, S. H., and Lin, T. Y. 2012. Empirical mode decomposition-based least squares support vector regression for foreign exchange rate forecasting. Econ. Model. 29, 2583–2590.
4. Huang, S. C., Chuang, P. J., and Wu, C. F. 2010. Chaos-based support vector regressions for exchange rate forecasting. Expert Syst. Appl. 37 (12), 8590–8598.
5. Dinger, Y., Li, S., and Li, L. 2009. An analysis on chaos behavior of currency exchange rate undulation. First International Workshop on Education Technology and Computer Science, Wuhan, Hubei, pp. 599–602.
6. Gradojevic, N., and Yang, J. 2006. Non-linear, non-parametric, non-fundamental exchange rate forecasting. J. Forecast. No. 25, 227–245.
7. Ridhwan, A., Kamel, M., Dahab, M. Y., and Hassanien, A., 2015. Forecasting exchange rates: a chaos-based regression approach. Int. J. Rough Sets Data Analysis 2 (1), 38–57
8. Chang P. H. K, and Melick, W. R. 1999. Workshop on Estimating and Interpreting Probability Density Functions. Bank for International Settlements Informations, Press Library Serv, 1 – 10.
9. Gurrola, P. 2008. Capturing fat-tail risk in exchange rate returns using SU curves: A comparison with the normal mixture and skewed Student distributions. J. Risk, 10, 73–100
10. Phoong, S. Y. and Phoong, S. W. 2022. A clustering analysis using finite mixture model. International Journal of Social Science Research, 4(2), 71-78.
11. Aitkin, M. and Rubin,D.B. 1985. Estimation and hypothesis terting in finite mixture models. Journal of the Royal Statistical Society B 47, 67-75
12. Atkinson,S. E. 1992. The performance of standard and hybrid EM algorithms for ML Estimation of the normal mixture model with censoring. Journal of Statistical Computation and Simulation 44, 105-115.
13. Atwood, L. D., Wilson, A. F., Bailey-Wilson, J. E., Carruth, J. N., and Elston, R. C. 1996. On the Distribution of likelihood ratio test statistic for a mixture of two normal distributions. Communications in Statistics-Simulation and Computation 25, 733-740.
14. Barndorff-Nielsen, O. 1965. Identifiability of mixture of exponential families. Journal of Mathematical Analysis and Applications 12, 115-121.
15. Basford, K. E. and McLachlan, G. J. 1985. Likelihood estimation for normal mixture models. Applied Statistics 34, 282-289.
16. Behboodian, J. 1970. On a mixture of normal distribution. Biometrika 57, 215-217.
17. Berdai, A. and Garel, B. 1996. Detecting a univariate normal mixture with two components. Statistics and Decisions. 16, 35-51.
18. Bezdek, J. C., Hathaway, R. M., and Huggins, V. J. 1985. Parametric estimation for normal mixture. Pattern Recognition 3, 79-84.
19. Blum, J. R. and Susarla, V. 1977. Estimation of a mixing distribution function. Annals of Probability 5, 200-209.
20. Brooks, S. P., Morgan, B. J. T., Ridout, M. S., and Pack, S. E. 1998. Finite mixture models for proportion. Biometrics 53, 1097-1115.
21. Campbell, N. A. 1984. Mixture models and atypical values. Mathematical Geology 16, 465-477.
22. Celeux, G. and Govaert, G. 1993. Comparison of the mixture and the classification maximum likelihood in cluster analysis. Journal of Statistical Computation and Simulation 47, 127-146.
23. Chandra, S. 1977. On the mixtures of probability distributions. Scandinavian Journal of Statistics: Theory and Applications 39, 105-112.
24. Choi, K. 1969. Estimators for the parameters of a finite mixture of distributions. Annals of the Institute of Statistical Mathematics 21, 107-116.
25. Day, N. E. 1969. Estimating the components of a mixture of two normal distributions. Biometrika 56, 463-474.
26. Delignette-Muller M. L, and Dutang, C. 2015. fitdistrplus: an R package for fitting distributions. J Stat Softw 64(4):1–34.
Downloads
Citation Tools
How to Cite
Salshabillah, C., Yendra, R., Desvina, A., ., R., & Marizal, M. (2023). Applied Some Mixture 2 and 3 Distribution for Daily Exchange Rate American Dollar vs Indonesian Rupiah Probability Modelling. International Journal Of Mathematics And Computer Research, 11(5), 3458-3464. https://doi.org/10.47191/ijmcr/v11i5.11
Most read articles by the same author(s)
- Masroh ., Rado Yendra, Ari Pani Desvina, Muhammad Marizal, The Applied of Functional Data Analysis to Comparison 100 Times Simulated Monthly Rainfall Using Some two Parameters Distribution , International Journal Of Mathematics And Computer Research: Vol 11 No 5 (2023): VOLUME 11 ISSUE 05
- Ernila Sari Gulo, Rado Yendra, Muhammad Marizal, Rahmadeni ., The Comparison some Models (Gamma, Slashed Quasi-Gamma, three Parameters Quasi Gamma, two Parameter Gamma-Exponential, and Modified Log-Logistic Distributions) for Daily Temperature Data , International Journal Of Mathematics And Computer Research: Vol 12 No 01 (2024): VOLUME 12 ISSUE 01