Gaussian_convergence_factor: Scaling factor where distribution converges to Gaussian

In niknap/ScalingFunctions: Collection of functions for scaling of distributions

Description

According to the central limit theorem distributions of aggregated variables converge to a Gaussian shape with increasing aggregation. This function calculates the aggregation factor between the current scale and the scale of convergence for a given data vector. It is based on the Berry-Esseen theorem, which provides an upper bound for the distance between standard normal CDF and z-transformed empirical CDF (based on the 3rd moment). This distance between CDFs is the Kolmogorov-Smirnov statistic D and for a desired significance level alpha the critical value of D can be calculated.

Usage

Gaussian_convergence_factor(vec, alpha = 0.05, BerryEsseen.const = 0.4748)

Arguments

vec	Input data vector
alpha	Significance level for the Kolmogorov-Smirnov statistic
BerryEsseen.const	Berry-Esseen constant (there are different values found in the literature)

Value

Scale factor between the current scale and the scale of Gaussian convergence (number of units that have to be aggregated, respectively)

Author(s)

Nikolai Knapp, [e-mail]

niknap/ScalingFunctions documentation built on May 22, 2021, 6:43 a.m.