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Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently. [ABSTRACT FROM AUTHOR]

In this study, we propose two estimators called the 3-step modified maximum likelihood (MML) and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators. [ABSTRACT FROM AUTHOR]

The use of wind as an energy source is becoming popular because of its non-polluting and renewable features. There is an urgent request to develop site-based estimation on wind engineering, which can be used for optimal design of wind turbines and wind farming. The wind speed for Zafarana Project in Suez Gulf, namely Site-3, based on monthly averaged data for 1 year as well as every 10 min for two days, one day in summer season and one day one winter season have been analyzed to estimate the most appropriate method to find Weibull distribution parameters for this site. The investigated methods are the mean wind speed method, the maximum likelihood method, the modified maximum likelihood method, the graphical method and the power density method. These methods results have been compared with the provided data to find their accuracy based on the root mean square errors. From the obtained results, the mean wind speed and the maximum likelihood method are recommended in estimating the wind speed distribution for the studied site in Zafarana wind farm. [ABSTRACT FROM AUTHOR]