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I have $(X, Y)$ data sets of two random variables. I want to apply copulas to obtain their joint probability distribution function. My data are highly skewed. In general, is it advisable to apply log transformation to the data? I see that by applying a log transformation to my data, I am getting nice histograms.

Also using those data sets, I have to estimate non-parametric kernel density estimates. Would log transformation help in getting better estimates of non-parametric kernel densities?

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    $\begingroup$ A transformation to the marginal distributions shouldn't change the dependence structure. What you're saying about KDEs doesn't make sense, though it seems like it warrants a separate question. $\endgroup$
    – Dave
    Commented Aug 27, 2020 at 16:17
  • $\begingroup$ Thanks, Dave. Actually I am talking about applying transformation to raw data itself. Regarding kernel densities, I want to know whether applying such a transformation would impact the estimates of KDEs?If yes, will those estimated KDEs would represent the true picture? $\endgroup$
    – Syed yunus
    Commented Aug 27, 2020 at 16:24
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    $\begingroup$ Of course the transformations impact the KDEs. The whole point of, say, a log transformation is to compress the tail. Now what do you mean by applying a transformation to the raw data if you're not applying transformations to the marginal distributions? $\endgroup$
    – Dave
    Commented Aug 27, 2020 at 16:27

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