Given a uniform list of numbers between 0 and 1, I would like to create a bell-shaped normal distribution.
So far, I:
- calculate the z-score for each element in the list (element - mean) / standard deviation
- I clamp the z-scores in the range [-2, 2] with MAX(-2, MIN(z, 2))
- I rescale each value to [0, 10] with ROUND((clampled_z/5+0.5)*10, 1)
The resulting shape is not convincing
I would like my bell shape to be fatter in the middle with few extrema values. I suppose I need to add some logarithm or exponential transformation to the dataset.
What would be a good way to rescale values proportionally closer to their mean value?
Thank you in advance for your suggestions
Not sure exactly what you need, but this may be helpful.
If you want to generate a random sample with a known CDF $F_X$ from a list of uniformly-distributed samples in $[0,1]$, then just apply $F_X^{-1}$ to each of the samples.
The resulting sample will be distributed like $X$.
In your case, if your uniformly-distributed samples are $x_1, x_2, x_3,\ldots$ then the transformed values $\Phi^{-1}(x_1), \Phi^{-1}(x_2), \Phi^{-1}(x_3)\ldots$ will be normally distributed.