# What type of function is this close to?

Does anyone recognize this type of function, or is this similar to another function?

I can see that it is discrete and that it has a point, (9, 30), where the function reflects and later repeats backwards.

This does not remind me about any function I know of, but as I enter more test values, it seems to approach a linear function.

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Quick guess: Looks like the sum of several delayed sigmoid functions ... – Dolma Apr 30 '13 at 16:33
Where do the results come from? Measurements or computations? I would suggest subtracting the linear trend (per linear regression and see if the remaining part resmbles something explainable. It could simply be an odd polynomial in $(x-9)$? – Hagen von Eitzen Apr 30 '13 at 16:34
The results come from computations, and every value is supposed to be an integer (although it is not possible to see that in the graph). Thank you for your advises, Dolma and Hagen von Eitzen! – Artem Apr 30 '13 at 16:40

As I said in my comment, this actually looks like the sum of delayed sigmoid functions.

If you denote $\sigma(x)=\dfrac{1}{1+e^{-x}}$ the logistic function. Looking at your plot, I thought of trying this function:

$$f(x)=\sigma(x-2)+\frac{1}{2}\sigma(x-9)+\sigma(x-17)$$

And here's the plot of this function:

So I guess you might want to look at this logistic function ;)

Note: You would just have to scale this up a little and change the inflection points positions (here $2$, $9$ and $17$) to fit your data.

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Thank you, Dolma! :) – Artem Apr 30 '13 at 16:41