scholarly journals A Note on the Existence of the Location Parameter Estimate of the Three-Parameter Weibull Model Using the Weibull Plot

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Chanseok Park
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Weibull Model ◽  
Parameter Estimate ◽  
Reliability Engineering ◽  
Bounded Interval ◽  
Weibull Plot ◽  
Sample Correlation

The Weibull model is one of the widely used distributions in reliability engineering. For the parameter estimation of the Weibull model, there are several existing methods. The method of the maximum likelihood estimation among others is preferred because of its attractive statistical properties. However, for the case of the three-parameter Weibull model, the method of the maximum likelihood estimation has several drawbacks. To avoid the drawbacks, the method using the sample correlation from the Weibull plot is recently suggested. In this paper, we provide the justification for using this new method by showing that the location estimate of the three-parameter Weibull model exists in a bounded interval.

scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

Maximum Likelihood Estimation with the Weibull Model

1974 ◽  
Vol 69 (345) ◽  
pp. 246-249 ◽  
Author(s):  
Howard Rockette ◽  
Charles Antle ◽  
Lawrence A. Klimko
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Weibull Model
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