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Each user's requirements are generated at random from the thresholded normal distribution defined by their individual PDS i function.
Although the demand patterns are smooth, individual user's PDS i functions inject noise into the simulation as a result of the random selection of product demands from the normal distribution.
In this simulation, we assume that user i has a product demand split that is generated from a normal distribution defined by its mean μ i, and its standard deviation σ I, with the value then thresholded to clip it within the range [0,8], i.e.: PDS i = min(max 0,N(μ i,σ i )),8).
The PLSPM analysis indicated a relatively strong relation between the IPDS and PDs, i.e. IPDS explains 41percentt of the variation in the PDs.
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The trend is first estimated by averaging PD i (f) over two periods: PD ⌢ i ( f ) = ∠ 1 M ∑ m ∈ C e j PD m ( f ) (17).
This trend is then removed before computing the standard deviation: σ i ( f ) = std i PD i ( f ) − PD ⌢ i ( f ) = − 2 log 1 M ∑ m ∈ C e j ( PD m ( f ) − PD ⌢ m ( f ) ) (18).
Nevertheless, the resulting PD i [ k] is still a circular data.
This phenomenon is revealed by PD i (2f0 t)) which tends towards low phase values.
Thus, over a few periods, PD i (f) has also a non-constant trend.
Figure 2 shows an example of PD i (2f0 t)) and the corresponding estimation of σ i (2f0 t)).
By replacing ϕi,h by its model Equation ??, the PD computation leads to: PD i, h = θ i, h + 1 − θ i, h − θ i, 1. (13).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com