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I know that, as long as the mean of the normal distribution is 0, it can be transformed to a gamma, however, I am not sure about the non-central ones.

Maybe it is some kind of non-central chi-squared distribution with 1 degrees of freedom, however I am not sure if it can be transformed to a gamma anymore.

Thank you for your help!

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    I guess it is crucial to specify what is meant by "transformed". Every continuous distribution can be "transformed" to/from a uniform distribution on $[0,1]$ by means of its cumulative distribution function. Is this sort of thing what you have in mind?2017-01-10
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    sorry. I meant transformed as "is". So the square of a standard normal is a gamma.2017-01-10
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    and I am thinking about the square of a standard normal as a gamma2017-01-10

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