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I have a set of data points looking as if they could follow a skew-normal distribution when plotted. The explicit way the data is generated is unknown, but 2 things are constant for each set {$x,y$} these constant parameters are: $T=4$, $L=2\pi/26$. Additionally, we know the value of a 3rd parameter $A=a*T$ for each curved plotted. The data plots are bellow:

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semi log plot of data

What type of function/fit can be used to reproduce this behaviour in terms of the parameters listed? I unsuccessfully tried $y(x)=1+a*e^{-(b*x+e^{-b*x})}$ the Gumbel distribution. The data for A=1..5 is here data.ods or csv here CSv format

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  • $\begingroup$ Can you provide the data on another way than data.ods ? I cannot download the data without the required password. $\endgroup$ Commented Feb 28 at 11:08
  • $\begingroup$ @JJacquelin I put also a link to csv format should work with no passwords at all or try here filebin.net/dlzjdtfifcol5euo $\endgroup$ Commented Feb 28 at 13:26

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In order to improve the fitting one can increase the number of adjustable parameters in the function. For example instead of $$y(x)=1+a\:\exp\left(-b\;x-e^{b\;x} \right)$$ which is equivalent to $$Y(x)=\ln\left(y-1\right)=\ln(a)-b\;x-e^{b\;x}$$ the next modified function gives much better result : $$y(x)=1+a\:\exp\left(-b\;x-c\;e^{p\;x}-d\;e^{q\;x }\right)$$ Or equivalently : $$Y(x)=\ln(y-1)=\ln(a)-b\;x-c\;e^{p\;x}-d\;e^{q\;x }$$ Result in case $A=1$ :

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