Can the Beta Distribution be Adjusted to Range from -A to A?

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The discussion centers on the possibility of adjusting the beta distribution to span from -A to A instead of the standard 0 to 1. A U-shaped distribution centered at 0, similar to the probability density function of a sine wave, is sought for modeling purposes. While the beta distribution can be modified for this range, participants are encouraged to provide more details for better assistance. The beta distribution is noted as the closest match found so far, but there is an interest in identifying other potential probability density functions that could also produce a U-shaped plot. The conversation highlights the need for additional information to explore alternative distributions effectively.
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I have is a distribution that is U-shaped, centered at 0, spanning from -A to A, and I want a means to model this, a beta distribution is the closest thing I have found to kinda do this

can the beta distribution be adjusted to range from -A to A as opposed to 0 to 1? any other suggestions as to distributions to use?
 
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You're going to need to post more details.
 
The probability density function of a sin wave is a U shaped distribution, let's say from -A to A, where A is the amplitude of the sin wave. The beta distribution is the closest thing to a U shaped distribution I have found when the parameters alpha and beta are less than 1. I have found a way to adjust the range of the beta distribution

however, what I want to know are there any other PDF distributions that generate a U shaped plot. Beta is the only one I have found so far, wasnt sure if there was an obscure one out there under my nose
 
Essentially, X~Uniform(domain) so you want to find the distribution of f(X). I can't help you anymore unless you give more information.
 

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