Having some days with no precipitation, means that the CDF will not cross the origin of the axes but will have some value (probability), even for 0mm of precipitation.

For example, I attached a random dataset of precipitation I created, which contains 10000 days of precipitation with values in the range [0mm,12mm) per day.

Following that, is a histogram of the precipitation values divided into 100 bins.

The third graph is the CDF for all the values. You can see that the CDF doesn't drop bellow ~0.013, because there is always a probability for zero precipitation.

Is this helpful, or did I misinterpret your question?

Dear Stamatios Petalas,

Thank you very much for your detailed response.

With best regards,

Firdos