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I have taken a few econometrics courses and I know some things about distributions; things like skewedness, kurtosis, ect. However, there are other areas regarding distributions that I know I am weak on. I am particularly confused with the great variety of distributions out there. Surely, there is a plethora of choices regarding distribution in the existing literature. So here is a small list of questions I'd like to resolve to narrow the scope as well as some other preferences.

Subject Matter

  • True population distributions vs small-medium sample-size distributions, sometimes the underlying assumptions change? (I believe the Mahalanobis Distance equation is an example of this, in some sample sizes it assumes a chi sq, others a fishers T?)

Application

  • Intend to use in conjunction with econometric analysis and/or machine learning

Preferences

  • Math literacy is not my strong point, prefer a book with conceptual explanation, not just a slew of equations
  • (optional) I use eviews and python, so if any book has companion data files using either of these packages, that would be a plus

Question: From the above, are there any suitable books for me? Thank you!

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    $\begingroup$ Your criteria cover a great deal of the field of statistics! If you could narrow the focus it might help get more useful responses. $\endgroup$ – whuber♦ Jan 30 '18 at 14:51
  • $\begingroup$ @whuber I was afraid that would be the case. I have updated the post with some added clarity to the main focus. $\endgroup$ – Arash Howaida Jan 30 '18 at 15:08
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    $\begingroup$ Thank you. Could you clarify what you mean by "true parameter distributions" and "small-medium distributions"? And could you explain the mechanism by which a distribution might "change"? $\endgroup$ – whuber♦ Jan 30 '18 at 15:13
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    $\begingroup$ It's important to change your post to clarify its meaning--many (most?) readers will not wade through these comments. $\endgroup$ – whuber♦ Jan 30 '18 at 15:25
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    $\begingroup$ If you really want to understand distributions in the long term it is much better to go via mathematical way. From measure theory standpoint, distribution is such a trivial thing. $\endgroup$ – mpiktas Jul 24 '18 at 7:01
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I think I know where you are coming from, and so I will recommend Statistical Rethinking, by Richard McElreath, since it helped me so much. It only assumes you are decently familiar with linear regression and at least some math.

It explains theories very clearly, elaborating on them as needed with pedagogical (read: excellent) examples, that also demonstrate the limits of all statistical models (which I think is crucial), and is decently thorough. Toward the middle you'll learn about the exponential family of distributions and the models they each define, and why to use them.

The only drawback to this book is that it does not go into time series models, since they are not its focus.

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