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Is there a distribution like in the picture? It don't need to be the same, but like the idea (postive mean, negative next to mean and zero against $-\infty$ and $\infty$). distribution

user93287
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There is not. Density functions are always non-negative.

André Nicolas
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  • Hmm ok. And is there a steadily function (not density function) which looks like this? – user93287 Sep 05 '13 at 17:02
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    What does steadily function mean? – André Nicolas Sep 05 '13 at 17:04
  • oh sorry, wrong word. I mean continuous function – user93287 Sep 05 '13 at 17:07
  • Plenty. Here is a suggestion. Take a positive $A$, like $4$, and look at $f(x)=(A-x^2)e^{-x^2}$. That will give you something that has a shape like yours, but is symmetric about the $y$-axis. To have $x=b$ as the axis of symmetry, replace $x$ everywhere by $x-b$. You can tweak this in various ways, by using $e^{-cx^2}$ intead of $e^{-x^2}$, or else use $e^{-c|x|}$. – André Nicolas Sep 05 '13 at 17:17
  • You are welcome. You will have to play with parameters to get the exact shape you want. We don't need to use $a-x^2$, we can use $a-dx^2$. Or $a-d|x|^{3/2}$. If you have a very particular shape in mind, you may have to play around with these ideas a bit, perhaps using a graphing program. – André Nicolas Sep 05 '13 at 17:32