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The following two figures are the pdf's of four parametric distributions and their corresponding cdf's. The most left-ward blue line is clearly not skewed, while the most right-ward orange line is positively skewed.

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It is very easy to see which pdf's are positively skewed, but not so apparent in their corresponding cdf's. The blue and orange cdf's have virtually the same curvature. (Note that a dataset containing all negative values could still have a positive skew in its distribution, so the position of a distribution on the real-number line is not indicative of skewness whatsoever.)

Are there tell-tale signs from a cdf's plot, or underlying statistics (without knowing the parameters of how they were constructed of course), that are clear give-aways as to a cdf being positively skewed?

Source

develarist
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    Surely, as you find by comparing cdfs below and above probability 0.5. Also as cdfs map one-to-one to pdfs, they preserve all information about distribution shape. , – Nick Cox Dec 05 '20 at 14:26
  • without reverting from the cdf back to the pdf though, the question is about observing the cdf only. "surely" what? – develarist Dec 05 '20 at 14:28
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    Start by thinking about simple cases. A uniform pdf maps to a linear cdf. Departures from uniformity mean convex and/or concave segments, and so on. Symmetric pdfs have implications too: start with what normal or logistic or Student's t distributions look like as cdfs. – Nick Cox Dec 05 '20 at 14:42
  • alright I see where you're going, but then the next part is comparing which of 2 cdf's is more skewed than the other based on their respective convex/concave segments – develarist Dec 05 '20 at 14:51
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    It's often hard to tell from pdfs which is more skewed, and that also depends on what you use to measure skewness. – Nick Cox Dec 05 '20 at 14:59
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    One way to evaluate skewness visually is to reflect the CDF (or the PDF, if you like) around a central location such as the median and overplot the two curves. – whuber Dec 05 '20 at 15:19
  • ok if the CDFs are overlayed on top of each other at a common central reference point, then is the more skewed CDF the one that vertically "out-grows" the other CDF more/first in the right-half of the graph, or is it the shorter one – develarist Dec 05 '20 at 15:23
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    It's not that simple: the graphs of the CDF $F(x) = \Pr(X\le x)$ and its reflection $G(x)=1-F(2m-x)$ (where $m$ is the median of $X$) may cross each other multiple times--even infinitely often. "Skewness," generally speaking, constitutes the myriad and various ways in which a variable's distribution may be asymmetric. A "skewness coefficient" is merely a numerical summary of asymmetry, and consequently is inadequate to express the full variety of possible asymmetries. See https://stats.stackexchange.com/questions/24853 for some interesting examples. – whuber Dec 05 '20 at 19:32

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