Some of our previous experimental work focused on corona discharges in hydrocarbon media. It has been shown that the discharge can be characterized by corona "impedance.'' The present article elaborates on this work and introduces complementary details. In a negative pin-to-plane geometry, the experiments show that a corona parameter exhibits quasi-linear variation with corona current. The discharge was studied in a medium with controlled pressure, temperature, and homogeneity of the sample. The results were reproducible on different concentrations of the hydrocarbon mixture used. A modeling of the observed phenomenological relation is discussed. It is believed that the present analysis can be useful in optimizing characteristics of pin-plane corona discharges in hydrocarbon media.