Stable root evaluation for inverse Gaussian sampling
= Stable root evaluation for inverse Gaussian sampling
{title2=$x_-=\frac{\mu}{1+t+\sqrt{t(t+2)}}$}
With $t=\mu Y/(2\lambda)$, the lower root is $\mu/(1+t+\sqrt{t(t+2)})$ and the upper root is $\mu^2/x_-$. Rationalizing the lower-root formula avoids subtracting nearly equal large numbers when $Y$ is large.