Using R to extract truncated normal distribution samples and normal distribution samples separately, when they are combined, the image drawn by the hist function is very similar to a normal distribution. What is the reason?
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Whether or not this distribution has a simple bell shape will depend very much on the parameters; it will typically be bimodal (with two local maxima rather than one single); in any case, the procedure to calculate it is described in The Sum of Values from a Normal and a Truncated Normal Distribution.
answered Mar 26, 2022 at 14:48