Fig. 1

Average width and coverage probability of selected gamma CIs for age-adjusted mortality rates: simulation scenario 1. Average CI width and coverage probability of the Anderson–Rosenberg, Tiwari, Fay–Kim, and Fay–Feuer gamma CIs is based on 500 simulations with 10,000 replications each for age-adjusted mortality rates R = ∑(w_i/P_i) D_i and is presented as a function of the coefficient of variation (CV) of the weights u_i = w_i/p_i. Age-adjusted rates are anchored around an overall crude all-cause mortality rate of 833.8 per 100,000 population and the US national age distribution in 2010–2019. A multinomial distribution was used to generate the D_i conditional on the total D = ∑D_i. Results in the top row are for an overall population size of P = 2400, corresponding to \({\mathbb{E}}\)(D) = 20, whereas those in the bottom row are for P = 1200, corresponding to \({\mathbb{E}}\)(D) = 10. For the latter, a truncated Poisson distribution was used in simulations to ensure the overall numerator count remained ≥ 10