Research Article

Geodesic Distance on Gaussian Manifolds to Reduce the Statistical Errors in the Investigation of Complex Systems

Table 74

Log-normal distributions with asymmetric noise. The noise is composed of the sum of two Gaussians. The first Gaussian has zero mean and standard deviation equal to 10% of the maximum value of the data distribution = 0, s1 = 10% max(distribution); the second Gaussian has the mean equal = 2(s1+s2) and standard deviation s2 = 20% max(distribution). The noise is composed of 1000 points; of these 80% of the points are sampled on the first Gaussian and the remaining on the second Gaussian. The noise has a positive mean because > 0.

ā€‰No NoiseNoise

Mode2.5762.890

Mean3.2504.587
2.7654.101

Trimmed Mean3.0523.845
2.0792.950

Winsorized Mean3.1004.097
2.2493.433