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I have a function which plots the distribution of ions emitted as a function of the angle of emission. To simulate the emission I would like to sample values according to the function, but I'm struggling to do so.

The function is: enter image description here

where theta_0 is a constant.

I've tried to use the inversion method, but I can't seem to get it to work.

Alex
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  • Can you include some code with what you tried so far? You can also add a tag with the programming language/tools that you use. – Octavian Mărculescu Nov 02 '22 at 14:20
  • Also, your question might be better suited for https://math.stackexchange.com/ – Octavian Mărculescu Nov 02 '22 at 14:22
  • I haven't actually got to the stage where I've used code for the problem yet, so you're probably right that I should post it on somewhere for maths. Thanks very much for the suggestion. – Alex Nov 02 '22 at 14:26
  • Is that supposed to be a density or a CDF? What's the range for Theta? What bounds are there for Theta_nought? – pjs Nov 02 '22 at 19:17
  • @pjs : `theta_0` is usually 18, according to the cross-post: https://math.stackexchange.com/questions/4567447/how-do-i-generate-numbers-according-to-a-parabolic-distribution – Peter O. Nov 02 '22 at 22:45
  • See: https://stackoverflow.com/questions/66874819/random-numbers-with-user-defined-continuous-probability-distribution/66875719 . It appears that the function above has a bounded domain [0, `theta_0`], and an upper bound of the maximum if `theta_0=18` is 82. – Peter O. Nov 02 '22 at 22:52
  • @PeterO. Still have no idea what the range of Theta is, nor whether this is a density or CDF. Makes a huge difference trying to set up a possible inversion. – pjs Nov 02 '22 at 23:28

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