Noncentral chi-squared distribution
= Noncentral chi-squared distribution
{title2=$\chi^2_\nu(\lambda)$}
If $Z_1,\ldots,Z_\nu$ are independent <standard normal random variables> and $\lambda=\sum_j\mu_j^2$, then $\sum_j(Z_j+\mu_j)^2$ has a noncentral chi-squared distribution with $\nu$ degrees of freedom and noncentrality $\lambda$. For $\lambda=0$ it reduces to the <chi-squared distribution>. Squaring a shifted <signed normal Wald statistic> gives the case $\nu=1$.