The statistics of microdischarges crossing the air gap between conductors and insulating polymers have been measured. Long tails of pulse‐amplitude and pulse‐time‐separation distributions have been observed and their nature examined. The long tails of time distributions followed quasiexponential behavior while the long tails of amplitude distributions satisfied a fractal power law. The transformation relations between both sets of statistics have been determined and their consequences discussed. The clearly resolved fractal long tails of amplitude distributions have not been observed so far and represent a new result in the statistical studies of microdischarges. Also the determined transformation relations between time and amplitude statistics bring a new insight into the studied phenomenon. ©1995 American Institute of Physics.