RMSE Frequency Weighting
Hello. I signed up to these forums trying to find a solution to this... relatively simple problem.
I'm trying to calculate the Root-Mean-Square Error of predicted and observed models (wind roses to be specific). The models each have several data points, and each data point has several values and frequencies.
Disregarding the frequencies this is an easy thing to solve.
observed_frequency: 100 050 010
observed_value: 0.5 0.3 0.5
predicted_frequency: 090 060 005
predicted_value: 0.4 0.5 0.3
But the data points all have different frequencies on both the observed and predicted models (wind doesn't blow evenly in all directions), I need to weigh the Error based on the observed and predicted frequencies, and this part has me a bit stumped. Do any of you have an idea how to accomplish this?
RMSE = (Sum((observed_value_p_i - predicted_value_p_i) ^ 2) / n_count_values) ^ (1 / 2)