A Note on Confidence Intervals for a Linear Function of Poisson Rates

Abstract

We consider three interval estimators for linear functions of Poisson rates: a Wald interval, a t interval with Satterthwaite's degrees of freedom, and a Bayes interval using noninformative priors. The differences in these intervals are illustrated using data from the Crash Records Bureau of the Texas Department of Public Safety. We then investigate the relative performance of these intervals via a simulation study. This study demonstrates that the Wald interval performs poorly when expected counts are less than 5, while the interval based on the noninformative prior performs best. It also shows that the Bayes interval and the interval based on the t distribution perform comparably well for more moderate expected counts.

Keywords:

• Jeffreys prior
• t distribution
• Wald interval

Mathematics Subject Classification:

• Primary 62F25
• Secondary 62H12

Notes

¹See page 50 of Motor Vehicle Traffic Accidents (2000) at http://www.txdps.state.tx.us/administration/driver_licensing_control/accident_records/mvta2000/mvta2000.pdf