For example, if I have a probability distribution function (say a gamma function) of a series (say a daily streamflow series), and maybe I have a few other related data (say daily series of precipitation, temperature, etc.), is it possible to make a forecast of that flow series using technique like ANN, Monte-Carlo simulation, and the forecasted series will obey the probability distribution function described above?
Certainly. Probably the simplest approach is the Monte Carlo simulation you mentions. You could easily do this in excel. Just use your model of daily stream flow to form a prediction based on precipitation and temperature, etc. Then use this prediction as the expected value in your assumed probability distribution and draw random outcomes from it. An ANN model works as well
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