Weighted Weibull distribution and its applications

In this thesis, some statistical properties of Weibull and weighted Weibull distributions are examined, and their relations with other distributions are investigated. Three different parameter estimation methods, maximum likelihood, least squares and weighted least squares, are used to obtain estimates of unknown parameters of both distributions. The performances of these estimation methods are compared with Monte-Carlo simulation study. Bias and mean square error are used as comparison criteria. Finally, in order to show the modeling performance of the weighted Weibull distribution against the Weibull distribution, the seasonal daily mean wind speed data of Sinop province are analyzed. As a result of this analysis, it is shown that the weighted Weibull distribution provides better modelling than the Weibull distribution using both statistical tests and graphical methods.