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Statistical Papers

, Volume 51, Issue 2, pp 325–336 | Cite as

Testing for the Marshall–Olkin extended form of the Weibull distribution

  • Chrys CaroniEmail author
Note

Abstract

Marshall–Olkin extended distributions offer a wider range of behaviour than the basic distributions from which they are derived and therefore may find applications in modeling lifetime data, especially within proportional odds models, and elsewhere. The present paper carries out a simulation study of likelihood ratio, Wald and score tests for the parameter that distinguishes the extended distribution from the basic one, for the Weibull and exponential cases, allowing for right censored data. The likelihood ratio test is found to perform better than the others. The test is shown to have sufficient power to detect alternatives that correspond to interesting departures from the basic model and can be useful in modeling.

Keywords

Weibull distribution Marshall–Olkin extension Proportional odds Likelihood 

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References

  1. Bennett S (1983) Analysis of survival data by the proportional odds model. Statist Med 2: 273–277CrossRefGoogle Scholar
  2. Buse A (1982) The likelihood ratio, Wald, and Lagrange multiplier tests: an expository note. Am Statist 36: 153–157CrossRefGoogle Scholar
  3. Economou P, Caroni C (2007) Parametric proportional odds frailty models. Commun Statist Simul Comp 36: 1295–1307zbMATHCrossRefMathSciNetGoogle Scholar
  4. Ghitany ME (2005) Marshall–Olkin extended Pareto distribution and its application. Int J Appl Math 18: 17–32zbMATHMathSciNetGoogle Scholar
  5. Ghitany ME, Al-Awadhi FA, Alkhalfan LA (2007) Marshall–Olkin extended Lomax distribution and its application to censored data. Commun Statist Theory Meth 36: 1855–1866zbMATHCrossRefMathSciNetGoogle Scholar
  6. Ghitany ME, Al-Hussaini EK, Al-Jarallah RA (2005) Marshall–Olkin extended Weibull distribution and its application to censored data. J Appl Stat 32: 1025–1034zbMATHCrossRefMathSciNetGoogle Scholar
  7. Ghitany ME, Kotz S (2007) Reliability properties of extended linear failure-rate distributions. Prob Eng Inform Sci 21: 441–450zbMATHCrossRefMathSciNetGoogle Scholar
  8. Lee ET, Wang JW (2003) Statistical methods for survival data analysis, 3rd edn. Wiley, Hoboken, NJzbMATHGoogle Scholar
  9. Lindsey JK (1996) Parametric statistical inference. Clarendon Press, OxfordzbMATHGoogle Scholar
  10. Marshall AW, Olkin I (1997) A new method of adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84: 641–652zbMATHCrossRefMathSciNetGoogle Scholar
  11. Pham H, Lai C-D (2007) On recent generalizations of the Weibull distribution. IEEE Trans Reliab 56: 454–458CrossRefGoogle Scholar
  12. Zhang T, Xie M (2007) Failure data analysis with extended Weibull distribution. Commun Statist Simul Comp 36: 579–592zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.National Technical University of AthensAthensGreece

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