Error Measures for Normal Random Variables

Four commonly used measures of error are the root mean square error (RMSE), the geometric mean error (GME), the mean radial error (MRE), and the circular or spherical error probable (CEP, SEP). Exact or approximate closed form expressions are given. for each for zero mean, normal random variables in two and three dimensions. Numerical comparison of the measures suggests the relationship GME ⩽ SEP(CEP) < MRE ⩽ RMSE.