The generalized extreme value distribution (GEVD) and various extreme value distributions are commonly applied in air pollution, telecommunications, operational risk management, finance, insurance, material sciences, economics, and hydrology, among many other industries that deal with extreme events. Extreme value distributions (EVDs) typically limit the distribution of maximum and minimum values for many random observations drawn from the same arbitrary distribution. Besides that, it is a crucial method for forecasting future events and emerged as critical method for predicting future events. As a result, prior research is required to select the best estimation method to obtain a reliable value for the parameters of extreme value distributions. This study provides an overview of three-parameter estimation methods based on goodness-of-fit statistics and root mean square error (RMSE). This paper reviewed and compared three estimation methods used to approximate values of parameters for simulated observations taken from the EVD and GEVD. The method of moments (MOMs), maximum likelihood estimator (MLE), and maximum product of spacing (MPS) were the methods investigated in this study. Our findings indicated that the MPS performed better based on the mean square errors (MSEs); meanwhile, the MPS had similar goodness-of-fit statistic values compared to the MLE.

The latest trend of air pollution and variables influencing the air quality in Malaysia are studied in this research since there have been changes recently. Living conditions and health have been negatively impacted by air pollutants. An important method utilised nowadays is time series modelling, which is able to forecast events in the future. In this research, forecasting used one-year hourly Air Pollution Index (API) information originating from a station in Klang, Malaysia. The API values were predicted via the Artificial Neural Network model (ANN) and Autoregressive Integrated Moving Average model (ARIMA). Each of the approach’s performance was assessed via the root means square error (RMSE), mean square error (MSE), and mean absolute error (MAE). The outcomes highlight the fact that compared to ARIMA, the ANN provided the lowest forecasting error to predict API. As such, the ANN may be regarded as a reliable predictive method to generate data for the general public regarding the status of air quality at a particular time.