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Reading https://seankross.com/2016/02/29/A-Q-Q-Plot-Dissection-Kit.html (one of the first results about interpreting qq plots) I find myself confused about the slope of the qq plot

It is my understanding that, to take a qq plot (for simplicity, with 100 samples), you take points (x,y)_i where x is the theoretical ith percentile and y is the empirical ith percentile (that is,the ith sample in order).

For me that seems to imply that a fat tailed distribution, having more probability mass at the tails, will "grow slower" at the tails. That is, to go from the 10th to the 11th percentile will take a smaller step, given that the region has more probability density

However, the article shows the exact reverse result!

fat tails and qq plot

A fat tails distribution has higher slope in the tails than in the middle! Why is this so? Were did I go wrong?

josinalvo
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    The histogram and the qq plot are telling you the same story. You have heavier tails than in a normal. That means higher bars in the tails of a histogram and steeper slopes in the tails of the qqplot. Otherwise your distribution is close to symmetric. That's a pretty normal (common) kind of non-normal (non-Gaussian) distribution. – Nick Cox Sep 22 '20 at 15:33
  • (In fact you copied that pair of graphs from the link, so they aren't your results at all.) – Nick Cox Sep 22 '20 at 15:34
  • But shouldn't the difference between the (say) 5th and 6th percentiles be smaller because the probability density in the region is bigger? – josinalvo Sep 22 '20 at 15:34
  • (yes, this is an image from the article. I am trying to wrap my head around it) – josinalvo Sep 22 '20 at 15:35
  • Some people prefer to say longer-tailed, meaning that each tail is pulled out compared with a normal. – Nick Cox Sep 22 '20 at 16:12

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