On the Trivariate Non-Central Chi-Squared Distribution

In this paper, we derive a new infinite series representation for the trivariate non-central chi-squared distribution when the underlying correlated Gaussian variables have tridiagonal form of inverse covariance matrix. We make use of the Miller´s approach and the Dougall´s identity to derive the joint density function. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, bivariate noncentral chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, non-central chi-squared distribution for an arbitrary covariance matrix seems intractable with the Miller´s approach.