Optimization is central to any problem involving decision making. Thearea of optimization has received enormous attention for over 30 years and it is still popular in research field to this day. In this paper, a global optimization method called Kerk and Rohanin’s Trusted Interval will be introduced. The method introduced is able to identify all local solutions by converting non-convex optimization problems into piece-wise convex optimization problems. A mechanism which only considers the convex part where minimizers existed on a function is applied. This mechanism allows the method to filter out concave parts and some unrelated parts automatically. The identified convex parts are called trusted intervals. The descent property and the globally convergent of the method was shown in this paper. 15 test problems have been used to show the ability of the algorithm proposed in locating global minimizer.

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The weather in Malaysia is characterised by two monsoons, namely, the southwest monsoon from May to September, and the northeast monsoon from November to March. Wind direction is essential in observing the weather patterns and global climate. In this study, our interest is on investigating the relationship of the wind direction data of Langkawi Island in Malaysia during the southwest monsoon from year 2019 to 2020. It is essential to highlight that wind direction data that is circular and this requires different statistical techniques from the techniques that are used to analyse linear data. In this paper, we model the relationship of wind direction data by using the bivariate functional relationship model with von Mises distribution. The magnificence of this model is that the existence of error terms in all variables is considered. When modelling the data, outliers of the wind direction data are identified by using the covratio method that considers row deletion. The covariance matrix of the parameter estimates of the data is obtained by using the Fisher information matrix. Also, the result is supported by the Q-Q plots of the von Mises that indicate the goodness-of-fit of the wind direction data to the von Mises distribution. Then, maximum likelihood estimation is used in obtaining the parameter estimates of the data and hence, the model of the wind direction data is attained. The implications of this study provides an improved comprehension of the behaviour of wind direction and may be used for the prediction of wind energy in future.

In this paper, a global optimization algorithm namely Kerk and Rohanin’s Trusted Region is used to find the global minimizers by employing an interval technique; with it, the algorithm can find the region where a minimizer is located and will not get trapped in a local one. It is able to find the convex part within the non-convex feasible region. This algorithm has descent property and global convergence. The numerical results have shown the algorithm has an outstanding capability in locating global minimizers.

One of the most prevalent and traditional uses of statistics in hydrology is flood frequency analysis. The flood can occur practically everywhere and is considered the leading cause of natural disaster death worldwide. This study aims to apply the flood frequency analysis of the Kelantan streamflow site to identify the optimal distribution that best fits the flood frequency data from the goodness-of-fit test (GOF). Five distributions were applied in this study; namely lognormal (LG), generalized extreme value (GEV), generalized Pareto (GP), log-Pearson three (L3) and generalized logistic (GL) distribution. to obtain the parameter estimates. The distribution performance evaluation is then performed utilizing the GOF and efficiency evaluations. The results indicate that the generalized GP distribution is the best possible function for determining the annual peak flow at the Kelantan streamflow site.