Estimation of Left Truncated Fréchet Distribution Parameters with Maximum Likelihood Method

Extreme events such as in insurance, economics, climatology, hydrology, and telecommunications are great to be approached with Generalized Extreme Value (GEV) Distribution. Fréchet distribution is one of the three types of GEV that has the largest shape parameter or is called heavy tail. In some study, sometimes there is a limitation on the data value for certain purposes. The existence of truncation of a data will make the distribution change as well. This study aims the left truncated Fréchet distribution, which means that it applied to values X > a, where a is a constant which is the left cut point for the variable X. The value of a used in this research is intended to eliminate data outliers. This study aims to estimate the left truncated Fréchet distribution using the Maximum Likelihood Estimation (MLE) method. MLE is the method to maximize the Likelihood function. The MLE method procedure is very simple and easy to understand than other methods. Moveover, the application of these data is using wind power generation data. The result shows that the estimated shape parameter is 4.67328 and the scale parameter is 105.917.