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Stochastic orders of the Marshall–Olkin extended distribution

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  • Nanda, Asok K.
  • Das, Suchismita

Abstract

A general method of introducing a parameter, called tilt parameter, has been discussed by Marshall and Olkin (1997) to give more flexibility in modelling. In this paper, we take the tilt parameter of the Marshall–Olkin extended family as a random variable. The closure of this model under different stochastic orders viz. ageing intensity order, likelihood ratio order, shifted likelihood ratio orders and shifted hazard rate orders is discussed.

Suggested Citation

  • Nanda, Asok K. & Das, Suchismita, 2012. "Stochastic orders of the Marshall–Olkin extended distribution," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 295-302.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:295-302
    DOI: 10.1016/j.spl.2011.10.003
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    References listed on IDEAS

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    1. S. Kirmani & Ramesh Gupta, 2001. "On the Proportional Odds Model in Survival Analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 203-216, June.
    2. Nanda, Asok K. & Bhattacharjee, Subarna & Alam, S.S., 2007. "Properties of aging intensity function," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 365-373, February.
    3. Chrys Caroni, 2010. "Testing for the Marshall–Olkin extended form of the Weibull distribution," Statistical Papers, Springer, vol. 51(2), pages 325-336, June.
    4. Shanthikumar, J. George & Yao, David D., 1986. "The preservation of likelihood ratio ordering under convolution," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 259-267, December.
    5. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
    6. Gupta, Ramesh C. & Lvin, Sergey & Peng, Cheng, 2010. "Estimating turning points of the failure rate of the extended Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 924-934, April.
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    Cited by:

    1. Diren Yeğen & Gamze Özel, 2018. "Marshall-Olkin Half Logistic Distribution with Theory and Applications," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 6(2), pages 407-416, December.

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