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Estimation procedures for a family of density functions representing various life-testing models

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Abstract

A family of density functions is considered which contains several life-testing models as specific cases. Uniformly minimum variance unbiased estimators are obtained for the positive and negative powers of the parameter, moments and reliability function. These general results provide the estimators for the specific models.

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References

  1. Bahadur RR (1957) On unbiased estimates of uniformly minimum variance. Sankhyā 18:211–224

    MATH  MathSciNet  Google Scholar 

  2. Bain LJ, Engelhardt M (1991) Statistical analysis of reliability and life-testing models. Marcel Dekkar, Inc., New York

    MATH  Google Scholar 

  3. Barlow RE, Proschan F (1965) Mathematical theory of reliability. John Wiley and Sons, New York

    MATH  Google Scholar 

  4. Basu AP (1964) Estimates of reliability for some distributions useful in life testing. Technometrics 6:251–219

    Article  Google Scholar 

  5. Davis DJ (1952) The analysis of some failure data. Jour. Amer. Statist. Assoc. 47:113–150

    Article  Google Scholar 

  6. Dyer DD, Whisenand CW (1973) Best linear unbiased estimator of the parameter of Rayleigh distribution. IEEE Trans R-22:229–231

    MathSciNet  Google Scholar 

  7. Gray HL, Watkins TA, Schucany WR (1973) On the Jackknife statistic and its relation to UMVU estimators in the normal case. Commun. Statist. 2:285–320

    Article  MathSciNet  Google Scholar 

  8. Johnson NL, Kotz S (1970) Continuous univariate distributions — I. John Wiley and Sons, New York

    Google Scholar 

  9. Lehmann EL (1983) Theory of point estimation. John Wiley and Sons, New York

    MATH  Google Scholar 

  10. Lehmann EL, Scheffé H (1950) Completeness, similar regions and unbiased estimation — 1. Sankhyā 12:305–340

    Google Scholar 

  11. Lehmann EL, Scheffé H (1955) Completeness, similar regions and unbiased estimation — 2. Sankhyā 15:219–236

    MATH  Google Scholar 

  12. Patel JK, Kapadia CH, Owen DB (1976) Handbook of statistical distributions. Marcel Dekker, Inc., New York

    MATH  Google Scholar 

  13. Patil GP, Wani JK (1966) Minimum variance unbiased estimation of the distribution function admitting a sufficient statistics. Ann. Inst. Statist. Math. 18:39–47

    Article  MATH  MathSciNet  Google Scholar 

  14. Polvko AM (1968) Fundamentals of reliability theory. Academic Press, New York

    Google Scholar 

  15. Pugh EL (1963) The best estimate of reliability in the exponential case. Operations Research 11:57–61

    Article  MATH  Google Scholar 

  16. Sathe YS, Varde SD (1969) Minimum variance unbiased estimation of reliability for the truncated exponential distribution. Technometrics 11:609–612

    Article  MATH  Google Scholar 

  17. Siddiqui MM (1962) Some problems connected with Rayleigh distribution. Jour. Res. Nat. Bur. Stand-D 66D:167–174

    MathSciNet  Google Scholar 

  18. Sinha SK (1986) Reliability and life testing. Wiley Eastern Limited, New Delhi

    Google Scholar 

  19. Tyagi RK, Bhattacharya SK (1989) A note on the MVU estimation of reliability for the Maxwell failure distribution. Estadistica 41:73–79

    MathSciNet  Google Scholar 

  20. Weibull W (1939) A statistical theory of the strength of materials. Ing. Velenskaps Akad. Handl. 151:1–45

    Google Scholar 

  21. Weibull W (1951) A statistical distribution function of wide applicability. Jour. Appl. Mech. 18:293–297

    MATH  Google Scholar 

  22. Zacks S (1971) The theory of statistical inference. John Wiley and Sons, New York

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Ch. Charan Singh University, 250 005, Meerut, India

    Ajit Chaturvedi & Uma Rani

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  1. Ajit Chaturvedi
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  2. Uma Rani
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Chaturvedi, A., Rani, U. Estimation procedures for a family of density functions representing various life-testing models. Metrika 46, 213–219 (1997). https://doi.org/10.1007/BF02717175

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