The statistical properties of the soft gamma repeater SGR J1550-5418 are investigated carefully.We find that the cumulative distributions of fluence,peak flux and duration can be well fitted by a bent power law,while the cumulative distribution of waiting time follows a simple power law.In particular,the probability density fnnctions of fluctuations of fluence,peak flux,and duration have a sharp peak and fat tails,which can be well fitted by a q-Gaussian function.The q values keep approximately steady for different scale intervals,indicating a scale-invariant structure of soft gamma repeaters.Those results support that the origin of soft gamma repeaters is crustquakes of neutron stars with extremely strong magnetic fields.