Research Article

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

Table 75

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 negative mean because < 0.

ā€‰No NoiseNoise

Mode2.5762.731

Mean3.2503.248
2.7653.257

Trimmed Mean3.0523.158
2.0792.372

Winsorized Mean3.1003.216
2.2492.646