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Platykurtic Distribution: Definition and Examples

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”).

platykurtic

Platykurtic (left) and leptokurtic (right).




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.
A uniform distribution.

A uniform distribution.



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”).

Image: Barnard.edu.

Image: Barnard.edu.



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.

References:
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.

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Platykurtic Distribution: Definition and Examples was last modified: October 12th, 2017 by Andale

4 thoughts on “Platykurtic Distribution: Definition and Examples

  1. Andale Post author

    I’ve read that article before. I do clarify the correct interpretation in the final section (Onto More Technical Stuff). “…technically, a platykurtic distribution is defined by the fact it has shorter tails than a normal distribution, not that its peak is higher. ”

    However, I’ve found when teaching that students in elementary statistics grasp the idea of a “peak” better than they can grasp “tailedness.” This is much the same concept as teaching young schoolchildren about “finding averages” instead of the more correct “arithmetic mean”. You don’t find out until you’re in college that “average” isn’t a correct term at all for anything mathematical! As this site is geared towards people learning about statistics, I chose to present the material in an-easy-to-understand format.

  2. Peter Westfall

    Well, I have never heard the “average” story. Sure average is a correct term; what on earth are you talking about? The sample average is the sum of the data values divided by how many there are. A simple math equation.

    A better analogy would be to tell students that “half of the data are higher than the average and half are lower.” That is the same type of misinformation as telling them that excess kurtosis less than zero implies a flat topped peak. It is simply misinformation; “Alternative facts.”

    Sure, the uniform distribution has negative excess kurtosis, and the uniform distribution is flat-topped. But that “logic” is the same as the following “logic”:

    “Well I know that all bears are mammals, therefore all mammals are bears. ”

    The beta(.5,1) distribution has an infinitely pointy peak and negative excess kurtosis. So, using the “bear logic,” one could say that negative excess kurtosis implies that the peak is infinitely pointy.

    Is it better to teach people “alternative facts” just so that they can understand them easily? I think not. It’s just a waste of time, for everyone. It’s a waste of time and energy to teach the incorrect info, it’s a waste of time and energy to learn the incorrect info, and it’s also a waste of time having to unlearn it and then re-learn it correctly later.

  3. Andale Post author

    “it’s a waste of time and energy to learn the incorrect info, and it’s also a waste of time having to unlearn it and then re-learn it correctly later.”
    I disagree. We do it all the time in education, in order to make things simple for early learners. For example:

    • The Earth is round (not true — it’s an oblate spheroid).
    • The tongue detects different tastes (not true — for example, sour taste is detected by proteins on the tongue, not the tongue itself).
    • Diamonds are made from coal (not true — it’s a much more complex process that involves from deep and fast volcanic eruptions magma that travel through diamond stability zones.

    We don’t teach it the “correct” way because we don’t want to put the cart before the horse and start teaching six year olds about proteins, the intricacies of volcanic eruptions and diamond formation and the difference between a sphere and an oblate spheroid.

    Your logic “Well I know that all bears are mammals, therefore all mammals are bears” doesn’t follow. That statement, applied to leptokutic distributions, would be ““Well I know that all leptokutic distributions have most of the data is in the tails; therefore all distributions that have most of the data in the tails are leptokurtic. ” Nowhere do I say that all heavy-tailed distributions are leptokurtic.