Recent space plasma observations have provided us with three-dimensional ve
locity distributions having multiple peaks. We propose a method for analyzi
ng such velocity distributions via a multivariate Maxwellian mixture model
where each component of the model represents each of the multiple peaks. Th
e parameters of the model are determined through an iterative nonlinear opt
imization technique, specifically the expectation-maximization (EM) algorit
hm. For the automatic judgment of the preferable number of components in th
e mixture model, we introduce a method of examining the number of extrema o
f a resulting mixture model. We show applications of our method to ion obse
rvations in the plasma sheet boundary layer (PSBL) and in the central plasm
a sheet (CPS) of the Earth's magnetotail. From an analysis of the PSBL and
CPS, low-energy ions that have properties similar to those of lobe ions wer
e detected also in the PSBL and CPS. In the PSBL, middle-energy ion compone
nt which is flowing dawnward and directed the neutral sheet was extracted.
We suggested that magnetic field fluctuations in the PSBL can be explained
only when the two ion components were properly treated.