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Started working on reconstruction

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Marius Drechsler 2024-07-19 17:45:34 +02:00
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@ -37,6 +37,6 @@ This transformation can be performed using the function $xi = tilde(x)$. The key
Considering a normal distribution, the CDF is defined as
$ xi(frac(x - mu, sigma)) = frac(1, 2)[1 + \e\rf(frac(x - mu, sigma sqrt(2)))] $
=== ECDF
==== ECDF
The eCDF is constructed through sorting the empirical measurements of a distribution @dekking2005modern. Although less accurate, this method allows a more simple and less computationally complex way to transform real valued measurements into the Tilde-Domain. We will mainly use the eCDF in @chap:smhd because of the difficulty of finding an analytical description for the CDF of a Gaussian-Mixture.