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Some results related to distribution functions of chi-square type random variables with random degrees of freedom

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The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type [수식] with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables Xi. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix

Abstract

The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type [수식] with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables Xi. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix

참고문헌 (8)

  1. W. Feller, "An Introduction to Probability Theory and Its Applications, vol II" (1971), John Wiley and Sons
  2. N. L. Johnson, "Continuous Univariate Distribution-2" (1970), A Wiley-interscience publication
  3. R. V. Hogg, "Introduction to Mathematical Statistics" (2005)
  4. L. Hung Tran, "Some results on random sum of independent random variables", Statistics and Probability Letters (2007)
  5. L. H. Tran, "On distribution function of chi-square with random degrees of freedom", Journal of Applied Mathematics (2007)
  6. E. A. Lebedev, "On new properties distributions of mathematical statistics, Probability Theory, Random Processes, Mathematical Statistics and Applications", Proceedings of the Intertional Conference in honor of 70 years Jubilee of Professor, Doctor of Physical and Mathematical Sciences Gennady Medvedev, pp.154~160 (2005)
  7. H. Robbins, "The asymptotic distribution of the sum of a random number of random variables", Bulletin of the American Mathematical Society, 54, pp.1151~1161 (1948)
  8. Random sum estimators and their efficiency, "Y. B. Shvetsov", Department of Mathematical Sciences, Montana State University, 1~20 (2004)

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