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We know that any normal distribution can be transformed into a t-distribution as shown in this post: Transformation of any normal distribution into a standardized t-distribution

My question is can we transform a t-distribution into a normal distribution?

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    $\begingroup$ What sort of transformations do you consider? One can always transform a distribution to another distribution via the quantile and inverse quantile functions. The transformation that you link to is of a different kind and involves the division by another random variable (which is actually not really a transformation). So could you be more specific about this. $\endgroup$ Aug 6, 2023 at 19:44
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    $\begingroup$ What you linked is not a transformation. What is your purpose? It sounds to me like the problem you're trying to solve is <X>, and you're wondering if <Y> is a good way to go about it. Is that fair? Because if your real question is "<X>?" then I would suggest only asking about that. As its written right now, the question appears to be an XY Problem. $\endgroup$ Aug 7, 2023 at 2:29
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    $\begingroup$ Such questions (about transforming specific distributions to Normality) are FAQs: see this site search for many variants and their answers. After performing such a transformation you can follow it with an arbitrary transformation of a Normal distribution to a Normal distribution. Conclusion: "this same construction gives many non-affine transformations that will map a variable X with any given continuous distribution into another variable that is identically distributed." $\endgroup$
    – whuber
    Aug 7, 2023 at 13:35

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