A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter

Kantar, Yeliz Mert; Şenoğlu, Birdal

doi:10.1016/j.cageo.2008.04.004

Cited by 83 publications

(49 citation statements)

References 24 publications

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“…The cumulative distribution function (cdf) of the Weibull random variable, widely-used in engineering fields [1,21,22] is given as follows:…”

Section: Lse Methods For Log-logistic and Weibull Distributionsmentioning

confidence: 99%

“…Since the parameters of the considered distribution are used for inference results regarding topics of interest, their estimation methods have received great interest in the literature. The maximum likelihood estimation (MLE) method has good theoretical properties for large sample sizes (n > 250) and is often preferred [1]. However, it can show poor performance for small sample cases [1,2], and the MLE also requires an iterative numerical method, such as Newton-Raphson, for most distributions.…”

Section: Introductionmentioning

confidence: 99%

“…The maximum likelihood estimation (MLE) method has good theoretical properties for large sample sizes (n > 250) and is often preferred [1]. However, it can show poor performance for small sample cases [1,2], and the MLE also requires an iterative numerical method, such as Newton-Raphson, for most distributions. Additionally, some research has been conducted to find the best linear unbiased estimators for distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, some research has been conducted to find the best linear unbiased estimators for distributions. However, the proposed estimators in the literature are generally computationally intensive and require numerical methods to obtain estimates [1]. On the other hand, a regression procedure based on a probability plot to estimate the parameters of statistical distributions is frequently used by practitioners since its implementation procedure is simple in the cases of complete and censoring data.…”

Section: Introductionmentioning

confidence: 99%

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Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters

Kantar

2016

MCA

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Many estimation methods have been proposed for the parameters of statistical distribution. The least squares estimation method, based on a regression model or probability plot, is frequently used by practitioners since its implementation procedure is extremely simple in complete and censoring data cases. However, in the procedure, heteroscedasticity is present in the used regression model and, thus, the weighted least squares estimation or alternative methods should be used. This study proposes an alternative method for the estimation of variance, based on a dependent variable generated via simulation, in order to estimate distributional parameters using the weighted least squares method. In the estimation procedure, the variances or weights are expressed as a function of the rank of the data point in the sample. The considered weighted estimation method is evaluated for the shape parameter of the log-logistic and Weibull distributions via a simulation study. It is found that the considered weighted estimation method shows better performance than the maximum likelihood, least-squares, and certain other alternative estimation approaches in terms of mean square error for most of the considered sample sizes. In addition, a real-life example from hydrology is provided to demonstrate the performance of the considered method.

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“…The cumulative distribution function (cdf) of the Weibull random variable, widely-used in engineering fields [1,21,22] is given as follows:…”

Section: Lse Methods For Log-logistic and Weibull Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters

Kantar

2016

MCA

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“…Since the ML method gives doubtful estimates when we estimate the location, the scale and the shape parameters simultaneously unless large samples ( n > 250 or so) are available, (see, Bowman & Shenton 2001, Kantar & Senoglu 2008. See also, the Introduction of Acitas, Kasap, Senoglu & Arslan (2013).…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

Estimation and Testing in One-Way ANOVA when the Errors are Skew-Normal

Çelik¹,

Şenoğlu²,

Arslan³

2015

Rev. colomb. estad.

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Estimación y pruebas de hipótesis en ANOVA a una vía cuando los errores se distribuyen como normal sesgados Abstract We consider one-way analysis of variance (ANOVA) model when the error terms have skew-normal distribution. We obtain the estimators of the model parameters by using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies (see, Tiku 1967). In the ML method, iteratively reweighting algorithm (IRA) is used to solve the likelihood equations. The MML approach is a non-iterative method used to obtain the explicit estimators of model parameters. We also propose new test statistics based on these estimators for testing the equality of treatment effects. Simulation results show that the proposed estimators and the tests based on them are more efficient and robust than the corresponding normal theory solutions. Also, real data is analysed to show the performance of the proposed estimators and the tests. Resumen Se considera el modelo de análisis de varianza a una vía (ANOVA) cuando los términos de error siguen una distribución normal sesgada. Se obtienen estimadores de los parámetros desconocidos mediante el uso de la metodología de máxima verosimilitud (ML). Se proponen nuevos estadísticos de prueba basados en estos estimadores. Los resultados de la simulación muestran que los estimadores propuestos y los tests basados en ellos son más eficientes y robustos que los correspondientes a las soluciones de la teoría normal. Un conjunto de datos real es analizado con el fin de mostrar el desempeño de los estimadores propuestos y sus tests relacionados.Palabras clave: ANOVA, estimación, normal sesgada, pruebas de hipóte-sis, robustez.a Professor.

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Evaluating the lifetime distribution parameters and reliability of products using successive approximation method

Guo,

Kong,

et al. 2024

Quality & Reliability Eng

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The Weibull distribution is an extensively used statistical model for analyzing the reliability of mechanical and electrical components. Due to the complexity of the nonlinear equations and the scarcity of failure data, the common method may not provide satisfactory results of the reliability. In this case, a new approach for Weibull parameter estimation and reliability analysis, based on successive approximation schemes, is presented. The shape and scale parameters are estimated by maximizing the likelihood functions, and the location parameter is obtained by constructing an approximate correction model between it and the failure data. In order to show the performance of the proposed method, an extensive Monte‐Carlo simulation study is conducted. Simulation results show that the proposed method provides better estimates and efficient confidence intervals for Weibull parameters. In addition, the proposed method works well in presence of small sample sizes. Finally, two real examples are analyzed to illustrate the application of the proposed method.

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A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter

Cited by 83 publications

References 24 publications

Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters

Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters

Estimation and Testing in One-Way ANOVA when the Errors are Skew-Normal

Evaluating the lifetime distribution parameters and reliability of products using successive approximation method

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