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