  Type I X-ray bursts in a low-mass X-ray binary (LMXB) are caused by unstable
nuclear burning of accreted materials. Semi-analytical and numerical studies of
unstable nuclear burning have successfully reproduced partial properties of
this kind of burst. However, some other properties (e.g. the waiting time) are
not well explained. In this paper, we find that the probability distributions
of fluence, peak count, rise time, duration and waiting time can be described
as power-law-like distributions. This indicates that type I X-ray bursts may be
governed by a self-organized criticality (SOC) process. The power-law index of
waiting time distribution (WTD) is around $-1$, which is not predicted by any
current waiting time model. We propose a physical burst rate model, in which
the mean occurrence rate is inversely proportional to time $\lambda\propto
t^{-1}$. In this case, the WTD is well explained by a non-stationary Poisson
process within the SOC theory. In this theory, the burst size is also predicted
to follow a power-law distribution, which requires that the emission area
possesses only part of the neutron star surface. Furthermore, we find that the
WTDs of some astrophysical phenomena can also be described by similar
occurrence rate models.
