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Inference on the parameters of two Weibull distributions based on record values

Author

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  • H. Zakerzadeh
  • A. Jafari

Abstract

The Weibull distribution is a very applicable model for the lifetime data. Therefore, comparing the parameters of two Weibull distributions is very important. However, there is not an appropriate method for comparing the shape or scale parameters in the literatures based on record values. In this paper, we have proposed a simple exact method for testing and constructing confidence interval for the ratio of shape parameters in two Weibull distributions. In addition, a simple exact method is proposed for inference about the common shape parameter. For comparing the scale parameters, we use the concepts of generalized confidence interval and generalized p value, and derive approaches when the shape parameters are equal or unequal. Also, we give a generalized approach for inference about the common scale parameter. At the end, we investigate inference about stress–strength reliability. Simulation results show that proposed approaches are satisfactory. All approaches are illustrated using a real example. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • H. Zakerzadeh & A. Jafari, 2015. "Inference on the parameters of two Weibull distributions based on record values," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 25-40, March.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:1:p:25-40
    DOI: 10.1007/s10260-014-0278-3
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    References listed on IDEAS

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    1. Ali Jafari, 2012. "Inferences on the ratio of two generalized variances: independent and correlated cases," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 297-314, August.
    2. Mahdi Teimouri & Arjun K. Gupta, 2012. "On the Weibull Record Statistics and Associated Inferences," Statistica, Department of Statistics, University of Bologna, vol. 72(2), pages 145-162.
    3. Friedrich, Thomas & Knapp, Guido, 2013. "Generalised interval estimation in the random effects meta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 165-179.
    4. K. Krishnamoorthy & Yong Lu, 2003. "Inferences on the Common Mean of Several Normal Populations Based on the Generalized Variable Method," Biometrics, The International Biometric Society, vol. 59(2), pages 237-247, June.
    5. Soliman, Ahmed A. & Abd Ellah, A.H. & Sultan, K.S., 2006. "Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 2065-2077, December.
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    Cited by:

    1. A. Asgharzadeh & A. Fallah & M. Z. Raqab & R. Valiollahi, 2018. "Statistical inference based on Lindley record data," Statistical Papers, Springer, vol. 59(2), pages 759-779, June.

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