Statistical Inference about the Shape Parameter of the New Two‐parameter Bathtub‐shaped Lifetime Distribution

The two-parameter Weibull distribution is the most popular model for material strength. However, it may not be a good model for all materials over a wide range of sizes. In this note, a comprehensive review of the known variations of the two-parameter Weibull distribution is provided to help providing better modeling. Over 20 variations are reviewed. The appropriateness of the variations is discussed as models for brittle versus ductile strength. A comparison study of a selection of the variations is also provided. It is hoped that this review will also serve as an important reference and encourage developments of further variations of the two-parameter Weibull distribution.

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“…ν → For further details of this distribution see Chen [16], Tang et al [17], Wu et al [18] and Nadarajah [19].…”

Section: Xie Et Al's Weibull Distributionmentioning

confidence: 93%

Strength modeling using Weibull distributions

Nadarajah

Kotz

2008

J Mech Sci Technol

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“…Consider the data given in Chen (2000 ) and Wu et al (2004) Chen (2000) that the 95% confidence interval for the shape parameter  is ( 0.19, 0.62 ) with interval length 0.43, based on a pivotal quantity for  . Wu et al (2004) proposed a new pivotal quantity for the shape parameter and evaluated the 95% confidence interval for the shape parameter as ( 0.27, 0.60 ) with interval length 0.33 which is shorter than Chen (2000) interval. Thus for purpose of comparison the 95% conditional confidence interval for the shape parameter is ( 0.35, 0.59 ) with interval length 0.24 .…”

Section: Examplementioning

confidence: 99%

“…Tang et al (2003) carried out in details the statistical analysis of this distribution and they derived the confidence intervals based on the asymptotic maximum likelihood estimates (AMLEs). Wu et al (2004) derived the exact confidence interval for shape parameter. Pham and Lai (2007) discussed most of the modifications for the Weibull distribution, and Silva et al (2009) derived the maximum likelihood estimates (MLEs) for the parameters of this model and presented some inferential procedures.…”

Section: Introductionmentioning

confidence: 99%

Conditional Inference for the Weibull Extension Model Based on the Generalized Order Statistics

Maswadah

El-Faheem

2018

Pak.j.stat.oper.res.

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In recent years, a new class of models has been proposed to exhibit the bathtub-shaped failure rate functions. The Weibull extension model is one of these models, which is asymptotically related to the ordinary Weibull model and is capable of modeling the bathtub-shaped and increasing failure rate lifetime data. This paper presents the conditional inference for constructing the confidence intervals for the Weibull extension parameters based on the generalized order statistics. For measuring the performances of this approach comparing to the Asymptotic maximum likelihood estimates, Simulation studies have been carried out, that indicated the conditional intervals possess a good statistical properties and they can perform quite well even when the sample size is extremly small. An illustrative examples based on real data are given to illustrate the confidence intervals developed in this paper.

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“…In recent years, the two parameter bathtub-shaped lifetime distribution has been studied by many authors, such as Lee et al [5] and Wu et al [6]. Also Rastogi et al [13] consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtubshaped distribution on the basis of progressive type-II censored sample by using different symmetric and asymmetric such as LINEX, entropy and squared error loss functions.…”

Section: Introductionmentioning

confidence: 99%