# Fitting a Distribution to Drought Data

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?

• 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. Commented Jul 1, 2023 at 17:19
• 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? Commented Jul 1, 2023 at 18:08
• 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. Commented Jul 1, 2023 at 18:41
• 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? Commented Jul 2, 2023 at 10:33