# Probability Distribution of the Monthly Average Buying Rate of Thai Baht to US Dollar

## Abstract

Exchange rate, especially the average buying rate of Thai Baht to US Dollar, is a financial index which plays an important role in Thai economy. The prediction of future average buying rate of Thai Baht to US Dollar would be very useful to investment planning and economic policies of Thailand. The probability distribution is one of the statistical models that can be used to predict average buying rate of Thai Baht to US Dollar. In this study, the appropriate distribution of the average buying rate of Thai Baht to US Dollar was obtained. Four types of probability distributions were investigated, i.e. normal distribution, log-normal distribution, gamma distribution and Weibull distribution. For goodness of fit test, Kolmogorov-Smirnov test and Anderson-Darling test were used and the root mean square error (RMSE) and the relative root mean square error (RRMSE) were criteria for measuring the prediction error of the appropriate distribution. The result indicated that the log-normal distribution was the most appropriate distribution of the average buying rate of Thai Baht to US Dollar compare to the others distributions. Keywords : monthly average buying rate ; normal distribution ; log-normal distribution ; gamma distribution ; Weibull distribution## References

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R Core Team. (2020). A language and environment for statistical computing. R Foundation for Statistical

Computing, Vienna, Austria. https://www.R-project.org/.

Sarpong, S. (2019). Estimating the Probability Distribution of the Exchange Rate Between Ghana Cedi and

American Dollar. Journal of King Saud University – Science, 31, 177-183.

Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Science (2nd ed.). New York:

McGraw-Hill.

Stephens, M. A. (1974). EDF Statistics for Goodness of fit and Some Comparisons. Journal of the American

Statistical Association, 69(347), 730-737.

Boothe, P. & Glassman, D. (1987). The statistical distribution of exchange rates: Empirical evidence and

economic implications. Journal of International Economics, 22(3-4), 297-319.

Chu J., Nadarajah S. & Chan S. (2015) Statistical Analysis of the Exchange Rate of Bitcoin. PLoS ONE, 10(7):

e0133678. DOI:10.1371/journal. pone.013367

Corlu, C.G. & Corlu, A. (2015) Modelling exchange rate returns: which flexible distribution to use?, Quantitative

Finance, 15(11), 1851-1864, DOI: 10.1080/14697688.2014.942231

Delignette-Muller, M.L. & Dutang, C. (2015). fitdistrplus: An R Package for Fitting Distributions. Journal of

Statistical Software, 64(4), 1–34. Retrieved May 10, 2020, from http://www.jstatsoft.org/v64/i04/.

Egan, W.J. (2007). The Distribution of S&P 500 Index Returns .Retrieved 6, 2007, from

https://ssrn.com/abstract=955639 or http://dx.doi.org/10.2139/ssrn.955639

Forbes, C., Evans, M., Hasting, N., & Peacock, B. (2011). Statistical Distributions (4th ed.). New York:

John Wiley & Sons.

R Core Team. (2020). A language and environment for statistical computing. R Foundation for Statistical

Computing, Vienna, Austria. https://www.R-project.org/.

Sarpong, S. (2019). Estimating the Probability Distribution of the Exchange Rate Between Ghana Cedi and

American Dollar. Journal of King Saud University – Science, 31, 177-183.

Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Science (2nd ed.). New York:

McGraw-Hill.

Stephens, M. A. (1974). EDF Statistics for Goodness of fit and Some Comparisons. Journal of the American

Statistical Association, 69(347), 730-737.

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## Published

2021-05-05

## Issue

## Section

Research Article