  We present a statistical analysis of the X-ray bursts observed from the 2002
June 18 outburst of the Anomalous X-ray Pulsar (AXP) 1E 2259+586, observed with
the Proportional Counter Array aboard the Rossi X-ray Timing Explorer. We show
that the properties of these bursts are similar to those of Soft
Gamma-Repeaters (SGRs). The similarities we find are: the burst durations
follow a log-normal distribution which peaks at 99 ms, the differential burst
fluence distribution is well described by a power law of index -1.7, the burst
fluences are positively correlated with the burst durations, the distribution
of waiting times is well described by a log-normal distribution of mean 47 s,
and the bursts are generally asymmetric with faster rise than fall times.
However, we find several quantitative differences between the AXP and SGR
bursts. Specifically, there is a correlation of burst phase with pulsed
intensity, the AXP bursts we observed exhibit a wider range of durations, the
correlation between burst fluence and duration is flatter than for SGRs, the
observed AXP bursts are on average less energetic than observed SGR bursts, and
the more energetic AXP bursts have the hardest spectra - the opposite of what
is seen for SGRs. We conclude that the bursts are sufficiently similar that
AXPs and SGRs can be considered united as a source class yet there are some
interesting differences that may help determine what physically differentiates
the two closely related manifestations of neutron stars.
