# How can Pareto(alpha = 5, x_min = 2) be heavy-tailed where alpha is the shape parameter or the tail index?

Point 1 : It's known that, usually, when the tail-index (alpha) is between 0 and 2, of a certain data set, the distribution is considered as heavy-tailed.

Point 2 : It's know that Pareto distribution is an example for heavy tailed distribution.

Let's consider Pareto distribution with alpha = 5 (say x_min = 2 for instance). Since 5 > 2, isn't point 2 become contradictory with point 1?

• The two points are using the term "heavy tailed" in distinctly different senses. – Glen_b Apr 2 at 8:21
• Do you mean, alpha in Pareto is different from alpha in a typical heavy-tailed distribution? – Dovini Jayasinghe Apr 2 at 9:57
• No. I literally mean what I wrote -- that the meaning of the phrase "heavy tailed" is different in those two points. – Glen_b Apr 2 at 11:25
• Could you please share some link or any source of information, where I can get the distinct meanings? Thank you for the feedback. – Dovini Jayasinghe Apr 3 at 4:58