The total_cases distribution for San Juan can be normalized well enough with a log transform, but its distribution for Iquitos seems hopelessly skewed. I have tried log, ln, squared, sqrt, inverse, and Box-Cox, to no avail. Has anyone found a good transformation?

This is because San Juan only has about 4% weeks with zero cases, but Iquitos has 18%!

There are just too many value that are equal, so I doubt any transformation will bring you normality from data is so bunched at a value. The data is telling you itâ€™s not a continuous distribution.

Can I ask you why do you want to put the total_cases into a normal distribution? Will you be using an estimation technique that requieres the output to be normal?