3458 Cantika Intan Salshabillah 1 , IJMCR Volume 11 Issue 05 May 2023 Volume 11 Issue 05 May 2023, Page no. – 3458-3464 Index Copernicus ICV: 57.55, Impact Factor: 7.362 DOI: 10.47191/ijmcr/v11i5.11 Applied Some Mixture 2 and 3 Distribution for Daily Exchange Rate American Dollar vs Indonesian Rupiah Probability Modelling Cantika Intan Salshabillah 1 , Rado Yendra 2 , Ari Pani Desvina 3 , Rahmadeni 4 , Muhammad Marizal 5 1,2,3,4,5 Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau ARTICLE INFO ABSTRACT Published Online: 30 May 2023 Corresponding Author: 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. KEYWORDS: Exchange Rate, micture distribution, Log-Normal, Gamma, Weibull I. INTRODUCTION Investors are very interested in the foreign exchange (forex) market because of the rapid growth of digitalization. Investors buy currencies from one country and exchange them for other currencies to take advantage of price fluctuations. When looking at a country's currency rate in the context of forex trading, one of the currencies that serves as a reference is the American Dollar, or USD rate. Other nations use the USD rate as a foreign exchange reserve rate. In a similar vein, the Indonesian Rupiah, or IDR rate, can be compared to the rupiah rate against the USD rate to assess its strength (Dewi et al., 2022). Additionally, Indonesia automatically evaluates its trade activities in USD currency because it is a partner in US export and import activities. Due to Indonesia's use of the US dollar for international trade [1,2], the USD plays an increasingly significant role. Because its trading activities are evaluated using the US Dollar (USD), an unstable Rupiah (IDR) exchange rate will typically interfere with trading because it can result in economic losses. An interesting topic to discuss is the significance of the exchange rate as an economic indicator. The probability of the exchange rate in the future is very important to discuss, and the exchange rate that changes actively results in the discussion of forecasting. Forecasting exchange rates is done by some researchers using statistical theory The Box-Jenkins approach to time series modeling and forecasting is utilized by many researchers. There are drawbacks to forecasting using the Box-Jenkins method. The existence of a linear relationship between the variables is assumed by this method. However, time series data are frequently nonlinear in the real world [3 - 6]. Second, utilizing the Box-Jenkins method for the model selection procedure is highly dependent on the researchers' expertise and experience [7]. The Box-Jenkins method's model selection procedure is highly dependent on the researcher's skill and experience. 2015. As a result, the accuracy of the Box-Jenkins method for modeling and forecasting is insufficient. All things considered, the paper analyzes the idea of probabilistic displaying, trailed by information. Because it is based on actual data, probabilistic modeling can be used to predict. In addition, they can instantly reflect data changes and do not necessitate lengthy historical time series for accurate estimation. Furthermore, probabilistic Muhammad Marizal