Abstract
A study is made of approximations for the central and noncentral bivariate chi-square distributions. In the former case the bivariate normal distribution is suggested for the approximation. Various power transformations are examined for this purpose. In the latter situation, the distribution is approximated by the central chi‐square distribution using: (i) results of Steyn and %%for the non-central Wishart distribution and (ii) a moment approximation similar to that suggested by Patnaik (1949) in the univariate case. The consequent normal approximations are directly applicable in this case too. Some numerical results illustrating the extent of the validity of the suggested approximations are given.
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