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Characterization of Normal Distribution Related to Two Samples Based on Regression

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Abstract

Characterization of normal distribution related to two samples based on second conditional moments has been obtained. This characterization has been transformed to a characterization based on the UMVU estimators of the density function. These results are generalized to k samples from normal distributions. Finally applications of these characterization results to goodness-of-fit test are discussed.

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References

  • D’Agostino RB, Stephens MA (1986) Goodness-of-fit techniques. Marcel Dekker, New York

    Google Scholar 

  • Gupta AK, Varga T (1990) Characterization of joint density by conditional densities. Commun. Statist. Theory Methods 19:4643–4652

    MATH  MathSciNet  Google Scholar 

  • Gupta AK, Nguyen TT, Wang Y (1997) Characterizations of some continuous distributions. J Ital Statist Soc 1:59–65

    MATH  Google Scholar 

  • Lehmann EL, Casella G (1998) Theory of point estimation. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Nguyen TT, Dinh KT (1998) Characterizations of normal distributions supporting goodness-of-fit tests based on sample skewness and sample kurtosis. Metrika 48:21–30

    Article  MATH  MathSciNet  Google Scholar 

  • Nguyen TT, Dinh KT (2003) Characterizations of normal distributions and EDF goodness-of-fit tests. Metrika 58:149–157

    Article  MATH  MathSciNet  Google Scholar 

  • Rao CR (1967) On some characterizations of the normal law. Sankhya A 29:1–14

    MATH  Google Scholar 

  • Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Statist 23:470–472

    MATH  MathSciNet  Google Scholar 

  • Singh J, Oliker VI (1979) On minimum variance unbiased estimation and characterization of densities. In: Proceedings of the Conference in Optical Methods in Statistics Academic, New York pp. 435–442

  • Wang Y, Gupta AK, Nguyen TT (1996) Characterization theorems for some discrete distributions based on conditional structure. Can J Stat 24:257–262

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Dhanuja Kasturiratna, Truc T. Nguyen & Arjun K. Gupta

Authors
  1. Dhanuja Kasturiratna
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  2. Truc T. Nguyen
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  3. Arjun K. Gupta
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Correspondence to Arjun K. Gupta.

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Kasturiratna, D., Nguyen, T.T. & Gupta, A.K. Characterization of Normal Distribution Related to Two Samples Based on Regression. Metrika 65, 43–52 (2007). https://doi.org/10.1007/s00184-006-0058-7

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  • DOI: https://doi.org/10.1007/s00184-006-0058-7

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