maximum likelihood method

Wind speed probabilistic distributions are one of the main wind characteristics for the evaluation of wind energy potential in a specific region.  In this paper, 3-parameter Log-Logistic distribution is introduced and it compared with six used statistical models for the modeling the actual wind speed data reported of Tabriz and Orumiyeh stations in Iran. The maximum likelihood estimators method via Nelder–Mead algorithm is utilized for estimating the model parameters. The flexibility of proposed distributions is measured according to the coefficient of determination, Chi-square test, Kolmogorov-Smirnov test, and root mean square error criterion. Results of the analysis show that 3-parameter Log-Logistic distribution provides the best fit to model the annual and seasonal wind speed data in Orumiyeh station and except summer season for Tabriz station. Also, wind power density error is estimated for the proposed different distributions.

The analysis of discrete mixed responses is an important statistical issue in various sciences. Ordinal and overdispersed binomial variables are discrete. Overdispersed binomial data are a sum of correlated Bernoulli experiments with equal success probabilities. In this paper, a joint model with random effects is proposed for analyzing mixed overdispersed binomial and ordinal longitudinal responses. In this model, we assume an overdispersed binomial response variable follows Beta-Binomial distribution and use a latent variable approach for modeling the ordinal response variable. Also, the model parameters are estimated via the Maximum Likelihood method, and the estimates are evaluated with a simulation study via the Monte Carlo method. Finally, an application of the proposed model to real data is introduced.