Exponentiated Weibull family for analyzing bathtub failure-rate data
TL;DR: In this article, a simple generalization of the Weibull distribution is presented, which is well suited for modeling bathtub failure rate lifetime data and for testing goodness-of-fit of the weibull and negative exponential models as subhypotheses.
Abstract: A simple generalization of the Weibull distribution is presented. The distribution is well suited for modeling bathtub failure rate lifetime data and for testing goodness-of-fit of the Weibull and negative exponential models as subhypotheses. >
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TL;DR: In this article, a three-parameter generalized exponential distribution (GED) was used for analysis of lifetime data, which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar et al.
Abstract: Summary The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.
1,084 citations
TL;DR: In this paper, the authors proposed to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number.
Abstract: The proportional hazards model has been extensively used in the literature to model failure time data. In this paper we propose to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number. This model gives rise to monotonic as well as non-monotonic failure rates even though the baseline failure rate is monotonic. The monotonicity of the failure rates are studied, in general, and some order relations are examined. Some examples including exponentiated Weibull, exponential, gamma and Pareto distributions are investigated in detail.
670 citations
TL;DR: The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function and can be considered as another useful 3-parameter generalization of the Weibull distribution.
Abstract: A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.
488 citations
Cites background from "Exponentiated Weibull family for an..."
...Unfortunately, the type-1 extreme-value distribution is not useful as a model for life distributions, because its support spreads over the whole real line....
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TL;DR: In this article, the authors define a family of univariate distributions generated by Stacy's generalized gamma variables and propose an expected ratio of quantile densities for the discrimination of members of these two broad families of distributions.
445 citations
Cites methods from "Exponentiated Weibull family for an..."
...When β = 1, it is the Exponentiated-Weibull family introduced by Mudholkar and Srivastava [20]....
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TL;DR: A new model, which is useful for modeling this type of failure rate function, is presented and can be seen as a generalization of the Weibull distribution.
441 citations
References
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Book•
01 Jan 1965TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Abstract: Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation. Large Sample Theory and Methods. Theory of Statistical Inference. Multivariate Analysis. Publications of the Author. Author Index. Subject Index.
8,300 citations
Book•
27 Nov 2002
TL;DR: Inference procedures for Log-Location-Scale Distributions as discussed by the authors have been used for estimating likelihood and estimating function methods. But they have not yet been applied to the estimation of likelihood.
Abstract: Basic Concepts and Models. Observation Schemes, Censoring and Likelihood. Some Nonparametric and Graphical Procedures. Inference Procedures for Parametric Models. Inference procedures for Log-Location-Scale Distributions. Parametric Regression Models. Semiparametric Multiplicative Hazards Regression Models. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models. Multiple Modes of Failure. Goodness of Fit Tests. Beyond Univariate Survival Analysis. Appendix A. Glossary of Notation and Abbreviations. Appendix B. Asymptotic Variance Formulas, Gamma Functions and Order Statistics. Appendix C. Large Sample Theory for Likelihood and Estimating Function Methods. Appendix D. Computational Methods and Simulation. Appendix E. Inference in Location-Scale Parameter Models. Appendix F. Martingales and Counting Processes. Appendix G. Data Sets. References.
4,151 citations
4,122 citations
2,421 citations