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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]

The Bayesian approach is applied to estimation of the Weibull-power law process (WPLP) parameters as an alternative to the maximum likelihood (ML) method in the case when the number of events is small. For the process model considered we propose to apply the independent Jeffreys prior distribution and we argue that this is a useful choice. Comparisons were also made between the accuracy of the estimators obtained and those obtained by using other priors—informative and weakly informative. The investigations show that the Bayesian approach in many cases of a fairly broad collection of WPLP models can lead to the Bayes estimators that are more accurate than the corresponding ML ones, when the number of events is small. The problem of fitting the WPLP models, based on ML and Bayes estimators, to some real data is also considered. It is shown that the TTT-concept, used in the reliability theory, is not fully useful for the WPLP models, and it may be so for some other trend-renewal processes. In order to assess the accuracy of the fitting to the real data considered, two other graphical methods are introduced. [ABSTRACT FROM AUTHOR]

In this study, the coefficients of Weibull Distribution Function (WDF) were calculated at two different heights using by six different methods. One-year wind data were used to determine the coefficients of WDF at different heights, and the wind data were obtained from a metrology station with a height of 10 m and a real wind turbine with a height of 80 m in Turkey's Hatay region. The used methods in this study were Graphical Method (GM), Empirical Method, Energy Pattern Method (EPM), Energy Trend Method, Maximum Likelihood Method and Moment Method.\ Three different statistical error analysis tests were used to compare the performance of the used methods at two different heights. Estimated mean wind speed and power values are the most important indicators to evaluate the performance of the used methods. In this study, mean wind speeds and powers were estimated in all methods for both heights using the WDF. These obtained values were compared with the actual real data and the best performing method was determined at both different heights for selected region. When the results were evaluated in general at both different heights, it was seen that the best performance method was the EPM and the worst performance method was the GM. [ABSTRACT FROM AUTHOR]

In this study, the potential of wind energy in Osmaniye Region has been analysed statistically on the basis of information that has been measured hourly between the years 2009 to 2013. The two-parameter Weibull Distribution Function is generally applied to evaluate the potential of wind energy in any region. This study introduced the evaluation of Weibull Distribution Function parameters which are obtained by different kinds of numerical methods, namely Graphical Method (GM), Moment Method (MM), Energy Pattern Method (EPM), Energy Trend Method (ETM), and Maximum Likelihood Method (MLM). The Relative Percentage Error (RPE) of statistical test is used to compare the efficiency of all used methods. The calculated power density of all used numerical methods is a major key issue for suitability use of wind energy. The evaluation of Weibull parameters and wind power distribution play a crucial role in producing electricity from wind power. The results of the used methods are compared, and the obtained pre-research results show that the wind energy potential in Osmaniye Region is statistically suitable for electricity production. [ABSTRACT FROM AUTHOR]

In this paper, a new life test plan called a progressively first-failure-censoring scheme introduced by Wu and Kuş [On estimation based on progressive first-failure-censored sampling, Comput. Statist. Data Anal. 53(10) (2009), pp. 3659–3670] is considered. Based on this type of censoring, the maximum likelihood (ML) and Bayes estimates for some survival time parameters namely reliability and hazard functions, as well as the parameters of the Burr-XII distribution are obtained. The Bayes estimators relative to both the symmetric and asymmetric loss functions are discussed. We use the conjugate prior for the one-shape parameter and discrete prior for the other parameter. Exact and approximate confidence intervals with the exact confidence region for the two-shape parameters are derived. A numerical example using the real data set is provided to illustrate the proposed estimation methods developed here. The ML and the different Bayes estimates are compared via a Monte Carlo simulation study. [ABSTRACT FROM PUBLISHER]

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]