If you want to fit your data with a probability distribution, I think just to start with a plot of historgram. The plot should give you an idea about a suitable distribution. I don't know any statistical test would help. In fact, there is a long-lasting debate in the statistic community about the validity of statistical tests.

Hello,

If you'll focused on Max values over 24 hours, The best technics in this area are: Extreme Values theory, the famous probability distribution are: generalized extreme value (GEV) distribution ; which combine the Gumbel, Fréchet and Weibull distributions.

Best Regards

Dear Wilmar Barbosa,

As your data are time-series, I suggest you do some Time series analysis to your data, and build a predictive model. There are different time-resies models you start with, for example Box–Jenkins Models for time series data can have many forms and represent different stochastic processes. These models are: autoregressive (AR) models, moving average (MA) models, autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models.

You can analyze your time-series data the above models in order to extract meaningful statistics and other characteristics of your data. Having done that, you can then buld a forecasting model to predict future values based on previously observed values.

Best wishes

Hola Wilmer, te recomiendo hacer todas las pruebas mencionadas anteriormente, esto lo puedes sacar fácilmente con un código en Python y mirar que se ajusta mejor a tus máximos .

Te envío unos links para que puedas mirar como generar tú código:

https://www.youtube.com/watch?v=JiKu6knMu-Q

https://www.youtube.com/watch?v=NeRjp3GIJgA&t=418s

Periodos de retorno:

https://www.youtube.com/watch?v=At77IKw0WSY

Saludos!

In addition to the GEV-distributions, you can also use these to set up intensity-duration-frequency (IDF) relationships. This can be combined with Peak-over-Threshold or yearly maximum series, attaining return period information.

If you want to check trends in the time series, the Mann-Kendall trend test is your best go to. If you'd like to check whether or not there are differences between the different stations in distributions, Kolmogorov-Smirnov is a popular test. This can also be used to test if the distribution at a station or more stations in general follows e.g. a certain distribution.