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We present a study of the waiting time distributions (WTDs) of solarenergetic 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 brokenpower-law WTD. The power-law index is $\gamma_{1} =$ 0.99 for the short waitingtimes ($<$70 hours) and $\gamma_{2} =$ 1.92 for large waiting times ($>$100hours). The break of the WTD of SEEs is probably due to the modulation of thecorotating interaction regions (CIRs). The power-law index $\gamma \sim$ 1.82is derived for the WTD of SPEs that is consistent with the WTD of type II radiobursts, indicating a close relationship between the shock wave and theproduction of energetic protons. The WTDs of SEP events can be modeled with anon-stationary Poisson process which was proposed to understand the waitingtime statistics of solar flares (Wheatland 2000; Aschwanden $\&$ McTiernan2010). 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 distributioncan produce a power-law tail WTD $\sim \Delta t^{\alpha - 3}$, where $0 \leq\alpha < 2$.

Waiting time distribution of solar energetic particle events modeled with a non-stationary Poisson process