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Optimal tests and estimators for truncated exponential families

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Abstract

Blackwell-Rao-Lehmann-Scheffe' theory is used to derive the minimum variance unbiased estimators for the functions of scale and truncation parameters as well as the reliability function of the truncated exponential family distribution. Uniformly most powerful unbiased tests of hypotheses are formulated. Finally, a particular model of this family, viz., the truncated exponential model is discussed.

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References

  • Cox, D.R., andD.V. Hinkley: Theoretical Statistics. London 1974.

  • Davis, R.C.: On minimum variance in non-regular estimation. Ann. Math. Statist.22, 1951, 43–57.

    Google Scholar 

  • Deemer, W.L. Jr., andD.F. Votaw Jr.: Estimation of parameters of truncated or censored exponential distributions. Ann. Math. Statist.26, 1955, 498–504.

    Google Scholar 

  • Ferguson, T.S.: Mathematical Statistics. A Decision Theoretic Approach. New York 1967.

  • Hogg, R.V., andA.T. Craig: Sufficient statistic in elementary distribution theory. Sankhya17, 1956, 209–216.

    Google Scholar 

  • Laurent, A.G.: Conditional distribution of order statistics and distribution of the reduced ith order statistic of the exponential model. Ann. Math. Statist.34, 1963, 652–657.

    Google Scholar 

  • Lehmann, E.L.: Testing Statistical Hypotheses. New York 1959.

  • Lwin, T.: Exponential family distribution with a truncation parameter. Biometrika62, 1975, 218–220.

    Google Scholar 

  • Park, C.J.: The Power Series distribution with unknown truncation parameter. Ann. Statist.1, 1973, 395–399.

    Google Scholar 

  • Quesenberry, C.P.: Transforming samples from truncation parameter distributions to uniformity. Commun. Statist.4 (12), 1975, 1149–1155.

    Google Scholar 

  • Sathe, Y.S., andS.D. Varde: Minimum variance unbiased estimation of reliability from truncated exponential distribution. Technometrics11, 1969, 609–612.

    Google Scholar 

  • Takacs, L.: On the method of inclusion and exclusion. J. Amer. Statist. Assoc.62, 1967, 102–113.

    Google Scholar 

  • Tate, R.F.: Unbiased estimation: functions of location and scale parameters. Ann. Math. Statist.30, 1959, 341–366.

    Google Scholar 

  • Washio, Y., H. Morimoto, andN. Ikeda: Unbiased estimation based on sufficient statistics. Bull. Math. Statist.6, 1956, 69–94.

    Google Scholar 

  • Zehna, P.W.: Invariance of maximum likelihood estimation. Ann. Math. Statist.37, 1966, p. 755.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Statistics, University of the Punjab (New Campus), Lahore, Pakistan

    M. A. Beg

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  1. M. A. Beg
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Beg, M.A. Optimal tests and estimators for truncated exponential families. Metrika 29, 103–113 (1982). https://doi.org/10.1007/BF01893370

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  • DOI: https://doi.org/10.1007/BF01893370

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