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If I have a random variable that has a Beta distribution multiplied by a scalar (say 1000), what is its distribution then? I have been doing some research and it appears not to be a beta distribution. Usually I use the distribution function to work out what the new parameters are, usually as the transformed distribution is from the same family as the original distribution, taking into account the constant being multiplied but seeing as the Beta distribution has an incomplete distribution function I am not sure how to approach this.

Please help and thanks!

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It doesn't have a beta distribution, since the new random variable is not almost surely in $[0, 1]$. It is a generalized beta distribution, as can be seen here.

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