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I am looking for a function looking similar to quadratic function but skewed to left; something like this:

enter image description here

Just ignore numbers and variables in the figure. I am interested only in the shape of the curve. The top does not have to be flat as in the figure. The point is that it is quadratic skewed to left. But I'm not using it as a probability distribution function. So it does not have to have properties of PDF. Actually, I would prefer not to.

Are there any function of this type?

ppp
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1 Answers1

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I sometimes use the Linex loss function when I want an asymmetric parabola:

$$f(x) = e^{ax} - ax - 1$$

for some constant $a$.

dshin
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  • Thanks so much. I flipped the function upside down and gave a positive y-intercept to make the function look like the curve in the figure. But I was not able to make curve start from the origin. Do you know how to do this? Thanks so much. – ppp Oct 13 '14 at 18:15
  • This should help: http://www.dummies.com/how-to/content/how-to-translate-a-functions-graph.html – dshin Oct 13 '14 at 18:28
  • Thank you. Can you suggest some way to modify the linear part of the equation so that it has a slight curvature when $0 < |x| < 1$ without a significant deviation of the slope from the linear case? – Ombrophile Oct 13 '21 at 06:17
  • @Ombrophile One side of the curve is approximately linear with slight curvature. – dshin Oct 13 '21 at 16:09
  • I see. Is it possible to add another parameter so that the curvature could be tuned even further? – Ombrophile Oct 14 '21 at 08:53