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In this paper: https://www.tandfonline.com/doi/pdf/10.1080/02664763.2021.1940109, the authors have two actual datasets (e.g., 59 observations showing continuous annual flood data) and the authors want to fit it with a Gumbel distribution.

The authors say that

"it is important to first have an idea of the underlying distribution of the two data sets. To get an idea of the underlying distribution of the two data sets, first construct a Q-Q plot by plotting the observed versus expected magnitudes, see Figure 1. "

enter image description here

Question: why can the author conclude that

It is clear from Figure 1 that the data points fall approximately on the straight line; therefore, it can be concluded that the extreme value distribution is an appropriate distribution for both flood data sets.

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    $\begingroup$ The observed quantiles, in the opinion of the author, match up with the theorized quantiles of this extreme value distribution being considered. Is your concern that you’re used to seeing normal QQ plots? Those might be the most common, but the idea applies to other distributions, too. $\endgroup$
    – Dave
    Commented Nov 28, 2022 at 23:10
  • $\begingroup$ @Dave So you are saying that for any dataset we can analyze whether it is our expected expectation by QQ plot? Can I ask, if the data is almost on a straight line, it means that the quantile of the data is consistent with the theoretical quantile? So the distribution of the data is same as our desired distribution? $\endgroup$
    – Hermi
    Commented Nov 29, 2022 at 0:48
  • $\begingroup$ @Hermi If it is close enough to the diagonal line then it is plausible that the sample data was drawn from a distribution which was or was close to the theoretical distribution. As ever with statistics, you can never be certain about this. $\endgroup$
    – Henry
    Commented Nov 29, 2022 at 0:53

1 Answer 1

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Those curves look close to the diagonal. The small apparent discrepancies in a tail do not look substantial to me.

As an illustration not using Gumbel data, here is an example of a normal distribution Q-Q plot using points drawn from R's rnorm function. You can see one extreme negative sample value but no even moderately extreme positive sample values in this particular sample; such things can easily happen with samples. Using different seeds would have produced different patterns but many of them would have similar sorts of small apparent discrepancies visible.

set.seed(2022)
X <- rnorm(50)
qqnorm(X, pch=3, col="blue")
abline(0,1, col="red")

Normal Q-Q Plot

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