Figure 2

Simulation for a bivariate normal distribution. The fraction of observations (1000 runs of 1000 observations each for each value of the standard deviation) meeting the ratiometric definition (with a stability of 0.135) is shown as a function of the average correlation coefficient for each standard deviation. The constant correlation coefficient in this figure under the assumptions of equal changes in the standard deviation can be shown (using probability calculus) to be a property of the multivariate normal distribution.