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I know the word normal distribution. But what does a statistician call it when the curve of the distribution tails less steeply (ie falls more gradually) to the left or right?

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    Do you mean "a positive/negative skew"? – Centaurus Oct 31 '15 at 16:53
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    I agree with Centaurus -- "skewed curve". – Hot Licks Oct 31 '15 at 20:08
  • Yes, the pictures tell me that I absolutly mean that. :D Please transfrom your comment to an answer. – buhtz Nov 1 '15 at 10:26
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Skew is the term that I learned in engineering school, 40-odd years ago. If the plot of a "smooth" frequency distribution is not perfectly symmetrical it is said to be skewed (or possess skewness) in one direction or the other. (I'm a little fuzzy on what goes on if the distribution "curve" is ragged.)

A distribution can be skewed due to a longer "tail" on one side or a fatter tail or both.

Skew is a convenient term since it's basic meaning is intuitive to anyone with good familiarity with English, even though the detailed technical definition is incredibly Greek.

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It's simply referred to as a long-tail[ed] distribution.

Wikipedia has:

In statistics, a long tail of some distributions of numbers is the portion of the distribution having a large number of occurrences far from the "head" or central part of the distribution. The distribution could involve popularities, random numbers of occurrences of events with various probabilities, etc.

A probability distribution is said to have a long tail if a larger share of population rests within its tail than would under a normal distribution. A long-tail distribution will arise with the inclusion of many values unusually far from the mean, which increase the magnitude of the skewness of the distribution. A long-tailed distribution is a particular type of heavy-tailed distribution.

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  • "Long-tailed" is referring to the deviation from "normal" ("normal distribution", that is), not the degree of skew. A normal distribution can still be skewed. – Hot Licks Oct 31 '15 at 20:11
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    No it can't. The equation demands that there is a line of symmetry in the graph: it's a translated even function. You're talking about a 'skew normal distribution' (a three word compound); there's no such thing as a skewed 'normal distribution' {Wikipedia}. Are you a mathematician? – Edwin Ashworth Oct 31 '15 at 21:25
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    @HotLicks I am a mathematician and I work with probability and I confirm that the normal distribution cannot be skewed. The probability distribution function is a Gaussian curve. – Matt Samuel Nov 1 '15 at 4:36
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    Certainly a distribution can be skew, that's a fine term. But then it's not a normal distribution anymore (there may be such a thing as a "skew normal distribution", but that's different from a normal distribution; everybody knows what you're talking about when you say "normal distribution."). – Matt Samuel Nov 1 '15 at 7:07
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    @Hotlicks anyway, I would probably use "asymmetrical" or "skew distribution." As far as I know this answer is fine though. A statistician has more use for precise names of distributions. I was just putting in my two cents to confirm that normal distribution has a standard meaning. – Matt Samuel Nov 1 '15 at 7:16

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