  We present numerical simulations of electron magnetohydrodynamic (EMHD) and
electron reduced MHD (ERMHD) turbulence. Comparing scaling relations, we find
that both EMHD and ERMHD turbulence show similar spectra and anisotropy. We
develop new techniques to study anisotropy of EMHD turbulence. Our detailed
study of anisotropy of EMHD turbulence supports our earlier result of k_par ~
k_perp^(1/3) scaling. We find that the high-order statistics show a scaling
that is similar to the She-Leveque scaling. We observe that the bispectra,
which characterize the interaction of different scales within the turbulence
cascade, are very different for EMHD and MHD turbulence. We show that both
decaying and driven EMHD turbulence have the same statistical properties. We
calculate the probability distribution functions (PDFs) of MHD and EMHD
turbulence and compare them with those of interplanetary turbulence. We find
that, as in the case of the solar wind, the PDFs of the increments of magnetic
field strength in MHD and EMHD turbulence are well described by the Tsallis
distribution. We discuss implications of our results for astrophysical
situations, including the ADAFs and magnetic reconnection.
