In health sciences many variables may exhibit half-normal distribution. For example an inflammation process regarding one cell type or population in a tissue sample. The lack of the inflammatory cells describes the lack of disease and with increasing cell count in a sample the disease process becomes more severe and finally terminal. Moreover, a mild disease (small cell count) is more common than severe disease (high cell count) and thus the distribution of cell count is half-normal.
Assuming I have a variable with half-normal distribution and another variable which is normally distributed. Is it valid to use Pearson correlation coefficient with these two variables?