A bayesian analysis of the annual maximum temperature using generalized extreme value distribution

The annual maximum temperature was modeled using the Generalized Extreme Value (GEV) distribution to Jijel weather station. The Mann-Kendall (MK) and Kwiatkowski Phillips, Schmidt and Shin (KPSS) tests suggest a stationary model without linear trend in the location parameter. The Kurtosis and the Skewness statistics indicated that the normality assumption was rejected. The Likelihood Ratio test was used to determine the best model and the goodness-of-fit tests showed that our data is suitable with a stationary Gumbel distribution. The Maximum Likelihood estimation method and the Bayesian approach using the Monte Carlo method by Markov Chains (MCMC) were used to find the parameters of the Gumbel distribution and the return levels were obtained for different periods.