Fatigue damage is an important cumulative effect of random loads, such as those caused by earthquakes, wind and waves. The widely used Palmgren-Miner rule provides a simple procedure to quantify the damage produced by complicated time histories if a satisfactory cycle counting method such as the rain-flow algorithm is available. A cost effective alternative is to assume a probability distribution of stress ranges and to use it to solve the cycle counting problem. The shapes of six commonly used distributions were compared with that of rain-flow stress ranges, and it was found that acceptable results can be expected only in stress histories of narrow to medium band widths. It was also found, however, that the damage computed on the basis of the Rayleigh distribution can be adjusted to provide results that accurately agree with those achieved using the rain-flow method.