Comparison of Estimation Methods for Inverse Weibull Distribution

Akgül, Fatma Gül; Şenoğlu, Birdal

doi:10.1007/978-3-319-73241-1_1

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…It should also be noted that there are many papers in which the performances of the different estimation methods for the parameters of a distribution are compared. One can see for example Mazucheli et al [21] and Akgul and Senoglu [22] in this context.…”

Section: Introductionmentioning

confidence: 85%

A Comparison of Different Estimation Methods for the Parameters of the Weibull Lindley Distribution

Acıtaş¹,

Arslan

2020

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

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In this study, we consider different estimation methods for the parameters of Weibull Lindley distribution introduced by Ashgarzadeh et al. [1]. In this context, maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cramer Von Mises (CVM) and Anderson Darling (AD) estimation methods are utilized. The main focus of this study is to examine performances of these estimation methods. For this purpose, we carry out a Monte-Carlo simulation study based on different parameter settings and various values of the sample size. Results show that the AD estimators are almost preferable. Two real life data sets taken from the literature are also considered at end of the study.

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Section: Introductionmentioning

confidence: 85%

A Comparison of Different Estimation Methods for the Parameters of the Weibull Lindley Distribution

Acıtaş¹,

Arslan

2020

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

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“…Traditional methods cannot be used to solve equation (11). We can use the Newton-Raphson method [18,19] to find a numerical solution of this nonlinear equation when the shape parameter is known, i.e.,…”

Section: Maximum Likelihood Estimation (Mle)mentioning

confidence: 99%

“…More recently, Lai et al [2] wrote a monograph that comprises all aspects concerning the Weibull distribution and its expansions. Moreover, for the relevant information and details on applications, we recommend the readers to read several studies proposed in [4,6,8,[11][12][13][14]. e Bayesian estimation is commonly used in various scientific areas [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

Almazah

Ismail

2021

Mathematical Problems in Engineering

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Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.

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Modified minimum distance estimators: definition, properties and applications

2021

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Estimating the location and scale parameters of a distribution is one of the most crucial issues in Statistics. Therefore, various estimators are proposed for estimating them, such as maximum likelihood, method of moments and minimum distance (e.g. Cramérvon Mises-CvM and Anderson Darling-AD), etc. However, in most of the cases, estimators of the location parameter μ and scale parameter σ cannot be obtained in closed forms because of the nonlinear function(s) included in the corresponding estimating equations. Therefore, numerical methods are used to obtain the estimates of these parameters. However, they may have some drawbacks such as multiple roots, wrong convergency, and non-convergency of iterations. In this study, we adopt the idea of Tiku (Biometrika 54:155-165, 1967) into the CvM and AD methodologies with the intent of eliminating the aforementioned difficulties and obtaining closed form estimators of the parameters μ and σ . Resulting estimators are called as modified CvM (MCvM) and modified AD (MAD), respectively. Proposed estimators are expressed as functions of sample observations and thus their calculations are straightforward. This property also allows us to avoid computational cost of iteration. A Monte-Carlo simulation study is conducted to compare the efficiencies of the CvM and AD estimators with their modified counterparts, i.e. the MCvM and MAD, for the normal, extreme value and Weibull distributions for an illustration. Real data sets are used to show the implementation of the proposed estimation methodologies.

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Comparison of Estimation Methods for Inverse Weibull Distribution

Cited by 5 publications

References 23 publications

A Comparison of Different Estimation Methods for the Parameters of the Weibull Lindley Distribution

A Comparison of Different Estimation Methods for the Parameters of the Weibull Lindley Distribution

Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

Modified minimum distance estimators: definition, properties and applications

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