Some results related to distribution functions of chi-square type random variables with random degrees of freedom
Bull. Korean Math. Soc. 2008 Vol. 45, No. 3, 509-522
Published online September 1, 2008
Tran Loc Hung, Tran Thien Thanh, and Bui Quang Vu
Hue University, Hue University, Hue University
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 $\chi_{N}^{2}=\sum_{i=1}^{N}X_{i}^{2}$ 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
MSC numbers : 60F05, 60E10, 60G50, 62E20
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