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as far as I have searched even we can obtain optimal lambda value to transform data to normal distributed with constant variance in box cox transformation method we may have not proper normal distributed data points. In short at the end we have just closer form of normal distribution. Well what happens if we apply box cox transformation multiple times? Make our data much Closer to normal distribution than previous case?

No sufficient information about that on internet or books...

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  • $\begingroup$ Perhaps you need to adjust for outliers AND/OR variance change detection as discussed here docplayer.net/… $\endgroup$ – IrishStat Apr 7 at 16:52
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    $\begingroup$ Because Box-Cox transformations apply only to non-negative numbers and always result in some negative numbers, this possibility is automatically precluded. You always could use power transformations or other linear transforms of Box-Cox transformations to produce non-negative numbers and repeat, and occasionally this can work--but the circumstances are extremely rare, require quite a few parameters to fit, and are difficult to interpret. $\endgroup$ – whuber Apr 7 at 16:56
  • $\begingroup$ Whuber, what if we sum the data with a positive constant while we have negative transformed variable? Thus our transtormed data would be positive and we would have a chance again to apply box cox transformation and make data much more closer to normal distribution. What do you say? $\endgroup$ – mertcan Apr 7 at 17:11
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    $\begingroup$ I already covered that situation in my previous comment. You can do whatever you want to re-express your variables--there's no need to stick to the Box-Cox family at all--but it's up to you to keep track of the parameters you have thereby introduced and to interpret the resulting (rather complicated) transformation. My experience is that iterating Box-Cox transformations never pays off, but it's possible there are situations where it could be a good choice. $\endgroup$ – whuber Apr 7 at 17:22
  • $\begingroup$ Why iterating box-cox transformation never pays off? What is the mathematical explanation of it whuber? $\endgroup$ – mertcan Apr 7 at 18:03

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