I have a dependent variable ($Y$) whose distribution is as shown below. In particular, the variable exhibits positive skewness, has a few negative values and many positive values (generally less than one), and peaks near zero. The distribution after log transformation ($\ln(1+Y)$) is very similar too.

enter image description here

Would OLS models be a good choice in this case, or are there any alternatives that would better fit the nature of the dependent variable?

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    $\begingroup$ That is the marginal distribution of the response, yes? But regression models do not make assumptions on the marginal distributions, only on the conditional distribution given the regressors! That can only be tested after fitting a model, by, say, plotting the residuals. So show us the residuals after a linear regression. $\endgroup$ Commented Nov 20, 2017 at 13:29
  • $\begingroup$ @kjetilbhalvorsen Hey can you expand a bit more on marginal distribution and conditional distribution? Maybe some links or articles? This is the first time I am hearing about it and before this I was only familiar of the distribution of variable like when we plot a distplot using Seaborn. $\endgroup$
    – spectre
    Commented Jan 6, 2022 at 11:21
  • $\begingroup$ @spectre: This will be treated in any introduction to probability, but see many posts on this site $\endgroup$ Commented Jan 9, 2022 at 14:30

1 Answer 1


Have you considered a Skewed Normal Distribution?

I believe that using this distribution you'll be able to account for the skewness of your variable, but keeping the parametric space of a Normal Distribution, which seems adequate here.

Also, one part of your question was already answered here: Skewness in dependent variable (OLS, Gauss Markov, non-normality)

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    $\begingroup$ Many thanks for the suggestion, worked very well. In fact, a skewed-t distribution fits better than a skewed normal distribution. $\endgroup$ Commented Nov 20, 2017 at 13:47

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