Kurtosis > Platykurtic Distribution
You may want to read this article first: What is Kurtosis?
What is a Platykurtic Distribution?
Platykurtic distributions have negative kurtosis. Kurtosis gives you an idea of how much of a “peak” your distribution has — kurtos is Greek for “humpbacked” or “convex.” Despite the origins of the word, kurtosis in statistics refers to — somewhat confusingly — data in the tail and not the peak. But in general, tails and peaks are symbiotic: reduce one, and the other increases (and vice versa).
- Platykurtic (negative kurtosis): most of the data is in the tails; very little data is in the peak, (“fat and flat”).
- Leptokurtic (positive kurtosis): the bulk of the data is in the peak, with very little in the tails (“tall and skinny”).
An example of a very platykurtic distribution is the uniform distribution, which has as much data in each tail as it does in the peak.
Comparison to the Normal Distribution
Kurtosis is actually measured against a normal distribution, which has a kurtosis of 3. A platykurtic distribution will have a value much lower than that, and the peak will be flatter. Notice that I said “much” lower: There’s no real cut-off for when a distribution is platykurtic, and when it isn’t. If your values are close to 3, then your distribution is nearly normal (“mesokurtic”).
Onto More Technical(?) Stuff
At StatisticsHowTo.com, my job is to try and make statistical terms as clear as intuitive as possible. But this article wouldn’t be complete without this note: technically, a platykurtic distribution is defined by the fact it has shorter tails than a normal distribution, not that its peak is higher. I find that most people (myself included), have a hard time wrapping their head around this fact; The human brain seems to be wired to detect “peaks” in a distribution, rather than tails, probably because the peak is right in the middle, or perhaps we just like looking at the center of things. Whatever the reason, it’s a lot more intuitive to think about shapes of distributions in reference to the peak, not the tails, so that’s why I talk about kurtosis in those terms.
I’ll be the first to admit that I’m technically incorrect, and there are many statistics professors reading this who are probably quite upset at the “factual inaccuracies” in this article. I’ll just say this:
- If you want a non-mathematical, intuitive explanation for platykurtic, you can stop here. The idea of it having a flat peak is really all you need to know.
- If your plan is to become a statistician, or you’re interested a more mathematical explanation, read the definitions below.
“For symmetric unimodal distributions…negative kurtosis indicates light tails and flatness” (DeCarlo).
” Accordingly, it is often appropriate to describe…a platykurtic distribution as “thin in the tails” (Wuensch)
To me, this is a glass half-empty or glass half-full argument. You say tomAYto, I say tomAHto. To me, light tails and flatness means…a flatter peak, or, if you like, “Fat and flat”. Feel free to disagree.
DeCarlo, L. 1997. On the Meaning and Use of Kurtosis Psychological Methods. Vol 2. No.3, 292-307.
Wuensch, K. Undated. Skewness, Kurtosis, and the Normal Curve.