How do we modify the tails of norrmal/any kind of distribution by keeping other portion is same?

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I want to generate random numbers several times with keeping pdf constant in the middle portion and changing the trail part pdf of both sides. The pdf curve can be symmetry or asymmetry, it doesn't matter.

Accepted Answer

Paul on 7 Sep 2022
Hard to say much, at least for me, without knowing more details about the starting PDF and how the tails are going to be modified.
One approximate approach that may be feasible is to form the CDF of the new PDF, either exactly or via numerical integration as the case may be, and then model the resulting CDF as a piecewise linear distribution

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More Answers (1)

Jeff Miller
Jeff Miller on 8 Sep 2022
As Paul says, the details are important because there are infinitely many ways to do what you are asking. One way to think about the problem is in terms of a mixture distribution. Your original distribution is a mixture of (say) 10% of scores from its low tail, 80% of scores from its middle, and 10% of its scores from its high tail. It would be possible to keep the same three ranges of scores but to rearrange the percentages from each range in any way you like as long as they add up to 100%.
Jeff Miller
Jeff Miller on 8 Sep 2022
Sure, that is easy. For X from 0 to 0.1, the PDF is 0.5. For X from 0.1 to 0.9, the PDF is 1. For X from 0.9 to 1, the PDF is 1.5. Note that the total area under the PDF is 1.

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