(untitled) (Journal of Academic Research, 2024)
Weibull distribution appears very frequently in practical when we observed data that represent extreme values. In this paper, the first objective is to identify the domain of attraction of a given distribution to belong in the domain attraction of maximum Weibull distribution by using Castillo and de Haan, necessary and sufficient condition. The second objective is used diagnostics plot by using three different plots, probability paper (P-P) plot, Quantile Quantile (Q-Q) plot and Return level (R-L) plot to detect an appropriate distribution of extreme. The third objective of the present study is to model the behavior of annual maximum temperature data by using maximum Weibull distribution. Maximum Likelihood Estimation (MLE) is used to estimate the parameters of distribution. The results show that the maximum temperature is significant to be fitted by max-Weibull model and it is the better choice basis on LR-test and graphical diagnostics. For the parameter estimation, LR-test and diagnostic plots calculations, we use the R programming language with packages of fExtreme and ismev to perform these calculations.