Parameter Estimation Of Weibull Distribution Research Articles

Analysis and Comparison of Weibull Parameters for Wind Energy Potential Using Different Estimation Methods: A Case Study of Isparta Province in Turkey

In this study, the success of the numerical methods and a metaheuristic algorithm in parameter estimation of Weibull distribution, which is frequently used in wind energy applications, are compared. Numerical methods are Justus empirical method, moment method, graphical method, energy pattern factor method (EPM), energy trend method, maximum likelihood estimation method (MLE). The metaheuristic algorithm is manta ray foraging optimization method (MRFO). The wind data used in the study were recorded hourly in the Isparta region in the southwest of Turkey. A graphical user interface design has been made to easily perform the calculations in this study. The success of the methods was tested with four different statistical error analysis methods. According to the results of the analysis, the MRFO method was by far the most successful method. EPM and MLE methods were the most unsuccessful methods.

Parameter estimation of Weibull distribution on type III censored survival data by maximum likelihood estimator method: Case study of lung cancer patient data at Dr. Kariadi Hospital Semarang

Research on survival data is quite important. Many modeling problems can be made related to survival data. One of the survival data methods is the Type III Censored method, which is a type of censoring that is limited by time, with individuals entering the study at different times during a certain period of time. In this study, the research focus is to obtain point estimates of the Weibull distribution parameters using the Maximum Likelihood Estimator method. The method is used to examine the survival data of Weibull distribution censored type III on secondary data of patients with lung cancer at Dr. Kariadi Hospital Semarang. Based on the results of the analysis, the Weibull distribution with a point estimator for the scale parameter is α̂ = 94.875997 and the shape parameter is β̂ = 1.638958.

Parameter estimation of Weibull distribution for the number of days between drug administration and early onset adverse event

ABSTRACT The Weibull distribution is applied to the number of days between the start date of drug administration and the date of occurrence of an adverse event. The tendency of occurrence of adverse events can be clarified by estimating the two- or three-parameter Weibull distribution, using the data regarding the number of days. Our purpose is to estimate the parameters of the Weibull distribution with high accuracy, even in low-reported adverse events, such as new drugs, polypharmacy and small clinical trials. Furthermore, the two-sample Kolmogorov – Smirnov test (two-sided) is used to examine whether the tendency of occurrence of adverse events is different for two Weibull distributions estimated from two drugs with similar efficacy. We used discrete data derived from FDA Adverse Event Reporting System (FAERS), as the FAERS data are presented in years, months and days without hours and minutes. Because this study focuses on early onset adverse events, data may be contained 0 days. The discreteness of the data and the fact that it may include zero make this distribution different from the general Weibull distribution, which is defined for continuous data greater than zero. We search for the optimal parameter estimation method for the Weibull distribution under these two conditions, and verify its effectiveness using Monte Carlo simulations and FAERS data. Because the results obtained from FAERS data may differ depending on data handling, we describe the of data handling technique and the sample code that can reproduce the results.

Study and early warning of comprehensive distribution box state based on maximum likelihood parameter estimation of Weibull distribution

With the expansion of the power grid scale and the improvement of distribution box automation, the structure of the distribution network has become more complex, and the maintenance task is heavy. The traditional post-maintenance and regular maintenance modes could not satisfy the requirements of distribution network equipment operation reliability. Firstly, according to the maintenance mode, the failure rate curve is proposed based on Weibull distribution. The service age reduction factor and the current failure rate of the equipment are mapped in this paper to the failure rate curve based on Weibull distribution. Secondarily, they are used to calculate the actual service age of equipment. The annual failure rate of equipment is used to count and determine the failure rate increment factor. Thirdly, the ant colony algorithm is applied to Weibull distribution maximum likelihood parameter estimation. Finally, an example analysis verified that the parameter accuracy of ant colony algorithm estimation is higher. Thus, the correctness of the state-based equipment failure rate estimation method is verified, which lays a foundation for the formulation of a maintenance plan.

Comparing the parameter estimation methods of Weibull distribution with censored lifetime

Weibull distribution is widely used in reliability engineering and lifetime analysis because of its flexibility in modeling both increasing and decreasing failure rate. Weibull distribution has shape parameter and scale parameter, and it is difficult to estimate the parameters due to the no-closed form of likelihood function. In recent years, there has been studied on the approximating parameter estimation methods based on the simulation. In this study, we use the approximating parameter estimation of Weibull distribution with censored lifetime. The methods which are applied in numerical example are Bayesian estimation method, maximum likelihood estimation, and Markov chain Monte Carlo. Accuracy of estimation methods is performed by the mean square errors of parameter estimator in simulation reducing the experiment time. In addition, it can be helpful to set the design of experiment considering the characteristics of Weibull distribution with censored lifetime.

３母数ワイブル分布の母数推定について 疲労寿命分布の母数推定に関連して 続報

In reliability analysis of machines and structural members, it is important to clarify the fatigue life distribution of these engineering items, and Weibull distribution is often accepted as the original distribution of the fatigue life. Although various kinds of estimation procedures have been developed on three parameters of Weibull distribution, the statistical properties of each estimated parameter still remain unsolved for any estimation method.The authors performed the parameter estimation by means of several methods and discussed on the distribution characteristics of estimates of Weibull parameters. In this study, three different kinds of estimation were made on each parameter of Weibull distribution, and, the estimates obtained from the respective methods, including those given in the previous paper, were compared with each other in particular attention to statistical properties such as convergency or distribution of estimates. Finally, the most preferable method for parameter estimation of Weibull distribution was selected and quantitative discussions were also performed on the sample size required to determine, experimentally, the parameter of the original distribution.