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I have a set of data of 5 members. based on some previous questions , I was expecting to see where my actual points are located on the graph. in my case I see the theoretical but not my points.

just to mention that my samples are :

336256 620316 958846 1007830 1080401

Nick Cox
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FabioSpaghetti
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    The big blue dot inside the grey area represents your data – kjetil b halvorsen Aug 06 '18 at 05:48
  • Thank you very much, but why is it only one point? I have 5 points, also how do I judge which theory fits better? – FabioSpaghetti Aug 06 '18 at 05:55
  • @kjetilbhalvorsen also one question , my goal was to compare log-normal with Weibull. but since in this graph there is little distinguish between them, I wanted to know, does the graph suit for this evaluation ? – FabioSpaghetti Aug 06 '18 at 07:41
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    Your small sample is actually negatively or left-skewed, so qualitatively inconsistent with a lognormal and with any kind of Weibull that might seem a plausible alternative to a lognormal. – Nick Cox Aug 06 '18 at 09:13
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    (ctd) Hence why would your data plot at all on the graph because the unlabelled $x$ axis appears to be skewness from 0 to about 4? – Nick Cox Aug 06 '18 at 10:48
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    @Nick Cox: Looking at the R code of `descdist` indicates that what is plotted on the `x ` axis is the square of skewness. – kjetil b halvorsen Aug 06 '18 at 19:57
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    @FabioSpaghetti: Apart from only 5 obs being very little to compare distribution models, the blue "obs" point on the graph is far away from the lines represention lognormal or gamma, on the graph it is said that weibull line is close to those two, so neither is a good descriptor. You need more data! – kjetil b halvorsen Aug 06 '18 at 19:59
  • Thank you guys for the comments, the data I have is only these and are produced over months and are not easily produceable – FabioSpaghetti Aug 07 '18 at 04:53
  • Is there a difference if I calculate skewness or its squared? – FabioSpaghetti Aug 07 '18 at 04:54
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    If you plot skewness, not its square, then positive and negative skewness are plotted separately. The sign of skewness is important information! What Cullen and Frey did presumably they should explain. – Nick Cox Aug 07 '18 at 08:05
  • @NickCox what is left skewed and what is right skewed ? – FabioSpaghetti Sep 19 '19 at 06:46
  • As in my earlier comments negative skewness means left skewness and positive skewness means right skewness, The terms "left" and "right" refer to the position of the peak of the distribution on a graph like a histogram with magnitude horizontal. There is plenty of small print: e.g. different measures of skewness do not always agree even on sign, – Nick Cox Sep 19 '19 at 07:13
  • @Fabio rather than asking multiple people essentially the same question via comments, why not post a question? (after the requisite amount of [search and research](https://stats.stackexchange.com/help/how-to-ask), naturally) – Glen_b Sep 20 '19 at 17:05
  • @Glen_b Sure, sorry about that – FabioSpaghetti Sep 21 '19 at 09:34

1 Answers1

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You should see only one point.

These plots show (squared) skewness and kurtosis. If you have one sample, then you will have one value of skewness and one value of kurtosis for that sample -- i.e. exactly one point for one sample of data, not one point per observation within that sample.

It's perhaps a pity these are now so often called Cullen & Frey graphs; this name doesn't convey the information that they are plots of sample skewness (squared in this particular instance) and sample kurtosis. While they were sometimes called Pearson plots, another fairly common prior term for them was skewness-kurtosis plots, which does at least say what you're looking at.

Fortunately the help on the function you used to produce the plot does explicitly refer to the plot as a skewness-kurtosis plot.

The plot won't tell you a lot about your data though.

With only 5 data points you cannot expect to get much value out of the values of skewness and kurtosis, since they will have very large sampling error. The data will be consistent with a very wide range of Pearson distributions.

As Nick Cox rightly points out, the sample skewness is negative, so you would be looking to flip any distributions you considered with positive skewness = though again, with so few points, distributions with quite noticeable positive skewness could produce a sample with negative skewness pretty easily, so we should not read much into this in either direction.

Glen_b
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  • Thank you very much ,when is skewness negative and when is it positive ? – FabioSpaghetti Sep 19 '19 at 06:52
  • For a Pearson plot (/"Cullen and Frey" plot), skewness is defined as a standardized third central moment -- see wikipedia on [population skewness](https://en.wikipedia.org/wiki/Skewness#Pearson's_moment_coefficient_of_skewness), and [sample skewness](https://en.wikipedia.org/wiki/Skewness#Sample_skewness); in either case you get a numeric value. Once you calculate the value it's easy to see whether it's negative or positive (or perhaps zero). – Glen_b Sep 19 '19 at 07:02