Confidence interval for a reciprocal rate ($[L,U]\mapsto [1/U,1/L]$)

If a positive rate $q$ has a confidence interval $[L,U]$, monotonicity transforms it into $[1/U,1/L]$ for the reciprocal mean $1/q$. This preserves the coverage event exactly and reverses the endpoints. It applies directly to mean exponential holding times.