Fig. 1
From: Mean and variance of ratios of proportions from categories of a multinomial distribution
The simulation results based on the multinomial distribution given by (n,0.25,0.5,0.25), where n ranges from 10 to 50. The mean and variance of the original ratios Z0 (squares) as well as modified ratios Z1 (red circles) are compared with models: the Taylor-series model (solid line), the modified ratio model (dashed line), and the corrected modified ratio model (dash-dot line). Additionally, in the upper plot, there is also information about the variable zeros on the secondary right axis (dots). In this case, the modified ratio model outperforms the Taylor series model for Z0 data. Additionally, the uncorrected modified ratio model describes the Z1 data very well