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> (So basically a bell curve with very thin tails.) Is this a concept that exists? I thought "thin tailed" and "fat tailed" were defined by contrast to a norma

> (So basically a bell curve with very thin tails.) Is this a concept that exists? I thought "thin tailed" and "fat tailed" were defined by contrast to a normal distribution.

Ma8ee 2y ago
I don't think that "Bell curve" should be interpreted strictly as a Gaussian in this context, but more literally as a curve with a shape resembling a bell.
rscho 2y ago
From a doc, it was just a figure of speech. Most docs have no idea what a statistical distribution is.
Unlisted6446 2y ago
I'm pretty sure, yes? Cauchy distribution and student-t have fatter tails than a standard normal distribution.
hydrogen7800 2y ago
Kurtosis[0] is a term I came across when dealing with random vibration analysis, but I understand very little if it. The idea of "moments"[1] of various orders to describe a shape of distribution is interesting in general. It sounds analogous to Fourier series, describing a shape/graph with a series of values. [0]https://en.m.wikipedia.org/wiki/Kurtosis https://en.m.wikipedia.org/wiki/Kurtosis [1]https://en.m.wikipedia.org/wiki/Moment_(mathematics) https://en.m.wikipedia.org/wiki/Moment_(mathematics)
- thaumasiotes 2y ago
  That says exactly the same thing I just said: > Excess kurtosis, typically compared to a value of 0, characterizes the “tailedness” of a distribution. A univariate normal distribution has an excess kurtosis of 0. Negative excess kurtosis indicates a platykurtic distribution, which doesn’t necessarily have a flat top but produces fewer or less extreme outliers than the normal distribution. For instance, the uniform distribution (ie one that is uniformly finite over some bound and zero elsewhere) is platykurtic. On the other hand, positive excess kurtosis signifies a leptokurtic distribution. The Laplace distribution, for example, has tails that decay more slowly than a Gaussian, resulting in more outliers. (Emphasis added.) You can't have a bell curve with thin tails, because a bell curve has standard tails by definition.
  - hydrogen7800 2y ago
    I wasn't trying to correct you. Just responding to your comment asking if this is "a concept that exists".

> (So basically a bell curve with very thin tails.) Is this a concept that exists? I thought "thin tailed" and "fat tailed" were defined by contrast to a normal distribution.

Ma8ee 2y ago

I don't think that "Bell curve" should be interpreted strictly as a Gaussian in this context, but more literally as a curve with a shape resembling a bell.

rscho 2y ago

From a doc, it was just a figure of speech. Most docs have no idea what a statistical distribution is.

Unlisted6446 2y ago

I'm pretty sure, yes? Cauchy distribution and student-t have fatter tails than a standard normal distribution.

hydrogen7800 2y ago

Kurtosis[0] is a term I came across when dealing with random vibration analysis, but I understand very little if it. The idea of "moments"[1] of various orders to describe a shape of distribution is interesting in general. It sounds analogous to Fourier series, describing a shape/graph with a series of values. [0]https://en.m.wikipedia.org/wiki/Kurtosis https://en.m.wikipedia.org/wiki/Kurtosis [1]https://en.m.wikipedia.org/wiki/Moment_(mathematics) https://en.m.wikipedia.org/wiki/Moment_(mathematics)

thaumasiotes 2y ago
That says exactly the same thing I just said: > Excess kurtosis, typically compared to a value of 0, characterizes the “tailedness” of a distribution. A univariate normal distribution has an excess kurtosis of 0. Negative excess kurtosis indicates a platykurtic distribution, which doesn’t necessarily have a flat top but produces fewer or less extreme outliers than the normal distribution. For instance, the uniform distribution (ie one that is uniformly finite over some bound and zero elsewhere) is platykurtic. On the other hand, positive excess kurtosis signifies a leptokurtic distribution. The Laplace distribution, for example, has tails that decay more slowly than a Gaussian, resulting in more outliers. (Emphasis added.) You can't have a bell curve with thin tails, because a bell curve has standard tails by definition.
- hydrogen7800 2y ago
  I wasn't trying to correct you. Just responding to your comment asking if this is "a concept that exists".