# Joint probability distribution function between different time-series clusters

I have 24-hour time-series data-sets for Solar Power and Power Consumption respectively for an entire year i.e 365x24 data set. Intuitively, the data set captures the variation of each of the quantities over seasons.

To reduce dimensionality of the data-sets I applied Principal Component Analysis(PCA) and applied different clustering algorithms to each dataset. After forming clusters, I picked the median representative from each and now I have a reduced set to work with. Depending on the number of elements in each cluster, I also created a relative discrete probability distribution over both the data sets.

How do I find a joint PDF of these clusters?

Power_consumption = 7 X 365 (7 clusters) Probability Distribution Function

Solar_power = 20 X 365 (20 clusters). Probability Distribution Function