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On Distributions With Periodic Failure Rate and Related Inference Problems

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Advances in Statistical Decision Theory and Applications

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

The connections between the Integrated Cauchy Functional Equation, “almost lack of memory” property of a distribution and periodic failure rate of a distribution are explained. Some properties of distributions with periodic failure rates are discussed. The one to one correspondence between the distributions with periodic failure rates and the distributions with the “almost lack of memory” property is studied following the work of Chukova, Dimitrov and others. Applications of these distributions to modeling of minimal repair systems and related inference problems are given.

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References

  1. Baxter, L. A. (1982). Reliability applications of the relevation transform, Naval Research Logistics Quarterly, 29, 323–330.

    Article  MathSciNet  MATH  Google Scholar 

  2. Chukova, S. and Dimitrov, B. (1992). On distribution having the almost lack of memory property, Journal of Applied Probability, 29, 691–698.

    Article  MathSciNet  MATH  Google Scholar 

  3. Chukova, S., Dimitrov, B. and Garriado, J. (1993). Renewal and nonhomogeneous Poisson processes generated by distributions with periodic failure rate, Statistics and Probability Letters, 17, 19–25.

    Article  MathSciNet  MATH  Google Scholar 

  4. Crowder, M. J., Kimber, A. C., Smith, R. L. and Sweeting, T. J. (1991). Statistical Analysis of Reliability Data, London: Chapman &; Hall.

    Google Scholar 

  5. Dimitrov, B., Chukova, S. and Khalil, Z. (1995). Definitions, characterizations and structural properties of probability distributions similar to the exponential, Journal of Statistical Planning and Inference, 43, 271–287.

    Article  MathSciNet  MATH  Google Scholar 

  6. Galambos, J. and Kotz, S. (1978). Characterization of Probability Distributions, Lecture Notes in Mathematics # 675, Berlin: Springer-Verlag.

    Google Scholar 

  7. Lau, K. S. and Prakasa Rao, B. L. S. (1990). Characterization of exponential distribution by the relevation transform, Journal of Applied Probability, 27, 726–729. [Addendum ibid. 29 (1992), 1003–1004.].

    Article  MathSciNet  MATH  Google Scholar 

  8. Lau, K. S. and Rao, C. R. (1982). Integrated Cauchy functional equation and characterizations of the exponential law, Sankhyä, Series A, 44, 72–90.

    MathSciNet  MATH  Google Scholar 

  9. Leemis, L. M. and Shih, L. H. (1993). Variate generation for Monte Carlo analysis of reliability and life time models, In Advances in Reliability (Ed., A. P. Basu), pp. 247–256, Amsterdam: North-Holland.

    Google Scholar 

  10. Marsagalia, G. and Tubilla, A. (1975). A note on the lack of memory property of the exponential distribution, Annals of Probability, 3, 352–354.

    Google Scholar 

  11. Prakasa Rao, B. L. S. (1995). On distributions with periodic failure rate and related inference problems, Key note address at the Conference “Statistical Inference in Life Testing and Reliability”, September 1995, Banaras Hindu University, Varanasi, India.

    Google Scholar 

  12. Prakasa Rao, B. L. S. and Ramachandran, B. (1983). On a characterization of symmetric stable processes, Aequationes Mathematicae, 26, 113–119.

    Article  MathSciNet  MATH  Google Scholar 

  13. Ramachandran, B. (1979). On the “strong memorylessness property” of the exponential and geometric probability laws, Sankhyā, Series A, 49, 244–251.

    MathSciNet  Google Scholar 

  14. Ramachandran, B. and Lau, K. S. (1991). Functional Equations in Probability Theory, Boston: Academic Press.

    MATH  Google Scholar 

  15. Ramachandran, B. and Prakasa Rao, B. L. S. (1984). On the equation, Sankhyā, Series A, 46, 326–338.

    MathSciNet  MATH  Google Scholar 

  16. Rao, C. R., Sapatinas, T. and Shanbag, D. (1994). The integrated Cauchy functional equation: Some comments on recent papers, Advances in Applied Probability, 26, 825–829.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Indian Statistical Institute, New Delhi, India

    B. L. S. Prakasa Rao

Authors
  1. B. L. S. Prakasa Rao
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Editor information

Editors and Affiliations

  1. Department of Math, Southern Illinois University, 62901-4408, Carbondale, IL, USA

    S. Panchapakesan

  2. Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    N. Balakrishnan

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© 1997 Birkhäuser Boston

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Prakasa Rao, B.L.S. (1997). On Distributions With Periodic Failure Rate and Related Inference Problems. In: Panchapakesan, S., Balakrishnan, N. (eds) Advances in Statistical Decision Theory and Applications. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2308-5_22

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  • DOI: https://doi.org/10.1007/978-1-4612-2308-5_22

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7495-7

  • Online ISBN: 978-1-4612-2308-5

  • eBook Packages: Springer Book Archive

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