Estimation of mixed exponentiated Weibull parameters in life testing

Abd-Elrahman, Ayman M.; Mohamad, Mustafa A.

doi:10.12988/imf.2016.6445

Cited by 2 publications

(2 citation statements)

References 6 publications

(13 reference statements)

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“…Table (4) displays the results of fitting multiple lifetime distributions to the Aarset data. The competitive distributions are the additive Weibull (AddW) in [24], the WEM in [6], the modified Weibull in [25], the exponential flexible Weibull Extension (EFWE) distribution in [3], the two-component mixtures of three-parameter Weibull (M3pW) (see, [11]), exponentiated Weibull (MEW) (common scale parameters in both components) (see, [26]), Burr type III (MBurrIII) (see, [27]) and WEM are fitted as well. A reduced version of MWEM is the two-component mixture of the Chen model when the scale parameter 𝛽 = 1 for both components (MWEMR1).…”

Section: Discussionmentioning

confidence: 99%

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Mohamed¹,

Ismail²,

Ismail³

2022

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Finite mixture models have been used in many fields of statistical analysis such as pattern recognition, clustering and survival analysis, and have been extensively applied in different scientific areas such as marketing, economics, medicine, genetics and social sciences. Introducing mixtures of new generalized lifetime distributions that exhibit important hazard shapes is a major field of research aiming at fitting and analyzing a wider variety of data sets. The main objective of this article is to present a full mathematical study of the properties of the new finite mixture of the three-parameter Weibull extension model, considered as a generalization of the standard Weibull distribution. The new proposed mixture model exhibits a bathtub-shaped hazard rate among other important shapes in reliability applications. We analytically prove the identifiability of the new mixture and investigate its mathematical properties and hazard rate function. Maximum likelihood estimation of the model parameters is considered. The Kolmogrov-Smirnov test statistic is used to fit two famous data sets from mechanical engineering to the proposed model, the Aarset data and the Meeker and Escobar datasets. Results show that the two-component version of the proposed mixture is a superior fit compared to various lifetime distributions, either one-component or two-component lifetime distributions. The new proposed mixture is a significant statistical tool to study lifetime data sets in numerous fields of study.

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Section: Discussionmentioning

confidence: 99%

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Mohamed¹,

Ismail²,

Ismail³

2022

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“…Many authors studied record values and the associated statistics such as [1][2][3][4][5][6]. Furthermore, there are several studies which discussed some inferential methods based on record values for the Rayleigh [7,8], Weibull [9], inverse Weibull [10,11], exponentiated Family [12,13], Lomax [14,15], power Lindley model [16], exponentiated Weibull [17,18], and normal distribution [19].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

Al-Duais

2021

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The essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential (WLINEX) loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the proposed method (WLINEX) in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error (SEL) loss function, and maximum likelihood estimation (MLE). The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability.

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Estimation of mixed exponentiated Weibull parameters in life testing

Cited by 2 publications

References 6 publications

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

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