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I would like to transform non-normal distribution to normal distribution, and back-transform to its original state (or at least close to the original state).

From this article, I've read that you can transform the distribution in to normal distribution by using Box-Cox method.

Question 1: How do I choose lambda parameter for Box-Cox function? In the article, it seemed that the author chose lambda parameter that minimizes standard deviation of the transformed data.

Question 2: How do I know if the transformed data is a good fit of the actual data? What should I do if its not?

Question 3: How do I back-transformed data into its original shape? I understand that there will be distortion within the back-transformed data.

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    $\begingroup$ 1. Much of the point of Box-Cox is that it estimates the transformation parameter for you. Best not to treat the results slavishly. If $\lambda$ is reported as say $-$0.08 or 0.1, use logarithms. 2. Success can be assessed by a normal quantile (probability) plot after transformation. 3. No point to this: you still have the original data. $\endgroup$
    – Nick Cox
    Commented Feb 17, 2019 at 7:39
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    $\begingroup$ For question #2, I would argue that the whole point of doing a transformation is to wind up with new values. After all, if you wanted to get a good fit of the actual data, you have the actual data! $\endgroup$
    – Dave
    Commented Apr 16, 2022 at 1:11

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Partially answered in comments:

  1. Much of the point of Box-Cox is that it estimates the transformation parameter for you. Best not to treat the results slavishly. If λ is reported as say −0.08 or 0.1, use logarithms. 2. Success can be assessed by a normal quantile (probability) plot after transformation. 3. No point to this: you still have the original data.

– Nick Cox

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