A normal approximation for the chi-square distribution

An accurate normal approximation for the cumulative distribution function of the chi-square distribution with n degrees of freedom is proposed. This considers a linear combination of appropriate fractional powers of chi-square. Numerical results show that the maximum absolute error associated with the new transformation is substantially lower than that found for other power transformations of a chi-square random variable for all the degrees of freedom considered (1⩽n⩽1000).