Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME RESULTS RELATED TO DISTRIBUTION FUNCTIONS OF CHI-SQUARE TYPE RANDOM VARIABLES WITH RANDOM DEGREES OF FREEDOM

  • Hung, Tran Loc ;
  • Thanh, Tran Thien ;
  • Vu, Bui Quang
  • Published : 2008.08.31

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 $X^2_N={\Sigma}^N_{i=1}\;X^2_i$ with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables $X_i$. 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.

Keywords

random sum;chi-square random variable with degrees of freedom

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