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A conditional limit construction of the normal probability density

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Summary

It is shown that a normal probability density can be characterized as a limit of conditional probability densities of i.i.d. uniform random variables.

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References

  1. Bartfai, P. (1972). On a conditional limit theorem,Progress in Statistics: Colloquia Mathematica Societatis János Bolyai, Vol.9-I, 85–91.

    MathSciNet  Google Scholar 

  2. Chernoff, H. (1952). A measure of asymptotic efficiency for tests of hypothesis based on the sum of observations,Ann. Math. Statist.,23, 493–507.

    Article  MathSciNet  Google Scholar 

  3. Choi, B. S. (1983). A conditional limit characterization of the maximum entropy spectral density in time series analysis, Ph. D. Dissertation, Stanford University, Stanford, California.

    Google Scholar 

  4. Feller, W. (1971).An Introduction to Probability Theory and Its Applications, Vol. 2, John Wiley and Sons, New York.

    MATH  Google Scholar 

  5. Gradshteyn, I. S. and Ryzhik, I. M. (1980).Tables of Integrals, Series and Products, Academic Press, New York.

    MATH  Google Scholar 

  6. Kagan, A. M., Linnik, Y. V. and Rao, C. R. (1973).Characterization Problems in Mathematical Statistics, John Wiley and Sons, New York.

    MATH  Google Scholar 

  7. Kullback, S. and Leibler, R. A. (1951). On information and sufficiency,Ann. Math. Statist.,22, 79–86.

    Article  MathSciNet  Google Scholar 

  8. Lanford, D. E. (1973). Entropy and equilibrium states in classical statistical mechanics,Statistical Mechanics and Mathematical Problems, Lecture Notes in Physics, No.20, 1–113, Springer-Verlag, Berlin.

    Google Scholar 

  9. Sanov, I. N. (1957). On the probability of large deviations of random variables,IMS and AMS Selected Translations in Mathematical Statistics and Probability, Vol.1, (1961), 213–244.

    MathSciNet  MATH  Google Scholar 

  10. Tjur, T. (1974).Conditional Probability Distributions, Institute of Mathematical Statistics, University of Copenhagen.

  11. Van Campenhout, J. M. and Cover, T. M. (1981). Maximum entropy and conditional probability,IEEE Trans. on Information Theory, Vol.IT-27, 483–489.

    Article  MathSciNet  Google Scholar 

  12. Vasicek, O. A. (1980). A conditional law of large numbers,Ann. Prob.,8, 142–147.

    Article  MathSciNet  Google Scholar 

  13. Vincze, I. (1972). On the maximum probability principle in statistical physics,Progress in Statistics: Colloquia Mathematica Societatis Janos Bolyai,9-II 869–893.

    MathSciNet  Google Scholar 

  14. Zabell, S. L. (1974). A limit theorem for conditional expectations with applications to probability and statistical mechanics, Ph. D. Dissertation, Harvard University, Cambridge, Mass.

    Google Scholar 

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Choi, B.S. A conditional limit construction of the normal probability density. Ann Inst Stat Math 37, 535–539 (1985). https://doi.org/10.1007/BF02481122

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  • DOI: https://doi.org/10.1007/BF02481122

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