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I'm trying to fit some distributions to a meteorological drought dataset. I had calculated the drought parameters from the SPI index, where i could define a dataset of the drought durations (in months) and it's respectively severity.

I'm working with the following dataset (n=30)

Drought Duration = 6, 7, 8, 22, 8, 7, 10, 8, 12, 12, 4, 3, 7, 4, 7, 1, 
    3, 10, 7, 9, 7, 3, 9, 8, 7, 11, 6, 8, 4, 7
Drought Severity = -1.98, -2.21, -3.91, -13.17, -0.75, -0.65, -1.59, 
    -2.95, -1.24, -3.09, -0.96, -1.45, -1.52, -2.86, -3.61, -1.33, 
    -0.60, -2.08, -3.38, -5.69, -1.54, -0.57, -4.68, -1.13, -0.86, 
    -4.58, -5.38, -2.73, -1.52, -3.02

I tried to fit the following distributions: Exponencial, GEV, Gumbel, Pearson Type III and Weibul, with the parameters calculated by L-Moments Method.

So, I find some issues in my fitting:

  1. For severity, can i change all my data to positive values. As the severity is always negative, i thought that work with absolute values is not a problem. Can i work with it?

  2. As you can see, the duration data have some duplicated values. When i do a P-P Plot for the data-set (Weibull plotting position), the plot shows some "steps", as expected. Is there a alternate way to work with these data?

  3. Some distributions, as Exponencial, show a "weird" fitting for duration dataset. I'm using the rate equal 1/location. Am i using some wrong parameters for distributions?

PP-Plot for each distribution (duration and severity)

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  • $\begingroup$ In all cases the fit is being driven by the outlier at (22,-13.17). Clearly, the GEV is providing the best visual fit. Compare metrics for accuracy and error for confirmation. $\endgroup$
    – user78229
    Commented Jul 1, 2023 at 17:19
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    $\begingroup$ How is the severity of a drought measured? (It seems likely to be correlated with duration, so that you would want to model them together.) And what do you want to do with the fit? $\endgroup$
    – Matt F.
    Commented Jul 1, 2023 at 18:08
  • $\begingroup$ the severity value is measured by a standardized index (SPI). When the SPI value is under 0, there is a drought. The seveiry is given by the SPI value itself. Yes, i want to model it together. It's for my research, which i will apply the copula function to these models. $\endgroup$
    – Lucas
    Commented Jul 1, 2023 at 18:41
  • $\begingroup$ Given that the SPI is a time series, and droughts are functions of it, a copula approach seems unlikely to work well. Maybe you could instead find a stochastic model of the SPI with good features, and calculate the droughts from that. But this comes back to the question — once you have a model of droughts in your research, what will you do with it? $\endgroup$
    – Matt F.
    Commented Jul 2, 2023 at 10:33

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