We present a study of the waiting time distributions ( WTDs ) of solar energetic particle ( SEP ) events observed with the spacecraft WIND and GOES .
Both the WTDs of solar electron events ( SEEs ) and solar proton events ( SPEs ) display a power-law tail \sim \Delta t ^ { - \gamma } .
The SEEs display a broken power-law WTD .
The power-law index is \gamma _ { 1 } = 0.99 for the short waiting times ( < 70 hours ) and \gamma _ { 2 } = 1.92 for large waiting times ( > 100 hours ) .
The break of the WTD of SEEs is probably due to the modulation of the corotating interaction regions ( CIRs ) .
The power-law index \gamma \sim 1.82 is derived for the WTD of SPEs that is consistent with the WTD of type II radio bursts , indicating a close relationship between the shock wave and the production of energetic protons .
The WTDs of SEP events can be modeled with a non-stationary Poisson process which was proposed to understand the waiting time statistics of solar flares ( Wheatland 2000 ; Aschwanden \& McTiernan 2010 ) .
We generalize the method and find that , if the SEP event rate \lambda = 1 / \Delta t varies as the time distribution of event rate f ( \lambda ) = A \lambda ^ { - \alpha } exp ( - \beta \lambda ) , the time-dependent Poisson distribution can produce a power-law tail WTD \sim \Delta t ^ { \alpha - 3 } , where 0 \leq \alpha < 2 .