Applied Some Mixture 2 and 3 Distribution for Daily Exchange Rate American Dollar vs Indonesian Rupiah Probability Modelling

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