scholarly journals Parameter Estimation and Applications of the Weibull Distribution for Strength Data of Glass Fiber

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yuxuan Wu ◽  
Hanyang Xie ◽  
Jyun-You Chiang ◽  
Gang Peng ◽  
Yan Qin
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Glass Fiber ◽  
Fiber Strength ◽  
Estimation Method ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Strength Data ◽  
Parameter Estimation Method

Glass fiber is a good substitute for metal materials. However, in the process of manufacturing, it is necessary to carry out sampling inspection on its tensile strength to infer its quality. According to previous literatures, the strength data can be well fitted by the Weibull distribution, while the poor parameter estimation method cannot obtain reliable analysis results. Therefore, a new parameter estimation method is proposed. Based on the simulation results, it is found that the proposed parameter estimation method outperforms the other competitors to obtain reliable estimates of the Weibull parameters. Finally, the proposed parameter estimation method is applied to two real data sets of glass fiber strength for illustration. The results of data analysis show that our proposed parameter estimation method is more suitable for these data sets than other estimation methods.

A novel parameter estimation method for the Weibull distribution on heavily censored data

2019 ◽  
pp. 1748006X1988764 ◽  
Author(s):  
Renyan Jiang
Keyword(s):  
Parameter Estimation ◽  
Censored Data ◽  
Estimation Method ◽  
Least Square ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Distribution Models ◽  
Data Set ◽  
Hybrid Censoring ◽  
Parameter Estimation Method

It is desired to build the life distribution models of critical components (which are assumed to be non-repairable) of a repairable system as early as possible based on field failure data in order to optimize the operation and maintenance decisions of the components. When the number of the systems under observation is large and the observation duration is relatively short, the samples obtained for modeling are large and heavily censored. For such samples, the classical parameter estimation methods (e.g. maximum likelihood method and least square method) do not provide robust estimates. To address this issue, this article develops a hybrid censoring index to quantitatively describe censoring characteristics of a data set, proposes a novel parameter estimation method based on information extracted from censored observations, and evaluates the accuracy and robustness of the proposed method through a numerical experiment. Its applicable range in terms of the hybrid censoring index is determined through an accuracy analysis. The experiment results show that the proposed approach provides much accurate estimates than the classical methods for heavily censored data. A real-world example is also included.

scholarly journals Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type-I and Type-II Censoring

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ehab M. Almetwally ◽  
Mohamed A. H. Sabry ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Sh. A. M. Mubarak ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Type I ◽  
Alpha Power ◽  
Type Ii ◽  
Censored Samples ◽  
Distribution Parameters

This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull (MOAPW) distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions.

scholarly journals A new inverse Weibull distribution: properties, classical and Bayesian estimation with applications

2021 ◽  
Vol 48 (3) ◽  
Author(s):  
Ahmed Z. Afify ◽  
◽  
Ahmed I. Shawky ◽  
Mazen Nassar ◽  
◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Large Samples ◽  
Mathematical Properties ◽  
Inverse Weibull Distribution

This article proposes a new extension of the inverse Weibull distribution called, logarithmic transformed inverse Weibull distribution which can provide better fits than some of its well-known extensions. The proposed distribution contains inverse Weibull, inverse Rayleigh, inverse exponential, logarithmic transformed inverse Rayleigh and logarithmic transformed inverse exponential distributions as special sub-models. Our main focus is to derive some of its mathematical properties along with the estimation of its unknown parameters using frequentist and Bayesian estimation methods. We compare the performances of the proposed estimators using extensive numerical simulations for both small and large samples. The importance and potentiality of this distribution is analyzed via two real data sets.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mohammed M. A. Almazah ◽  
Muhammad Ismail
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Mean Square ◽  
Two Parameter

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.

scholarly journals Generalized Beta-Exponential Weibull Distribution and its Applications

2020 ◽  
Vol 24 (1) ◽  
pp. 1-33
Author(s):  
N. I. Badmus ◽  
◽  
Olanrewaju Faweya ◽  
K. A. Adeleke ◽  
◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Hazard Functions ◽  
Generalized Distributions

In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entropy and quantile function. Estimation of model parameters through maximum likelihood estimation method and observed information matrix are derived. Thereafter, the proposed distribution is illustrated with applications to two different real data sets. Lastly, the distribution clearly shown that is better fitted to the two data sets than other distributions.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

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