The frequency distribution of deep earthquakes (d>350 km) is analyzed on a regional scale, using magnitude data from ~4660 events reported in the International Seismological Center Bulletin (1964--1982) and 391 centroid moment tensor solutions (1977--1987). We use the moment magnitude Mw to define b values comparable with studies of shallow seismicity; scaling laws relating Mw, mb, and M0 are derived (Mw=1.6mb-3.2; mb=M0-4.3>/2.4) which compare very favorably with published laws. Uncertainties and biases of the mb and M0 data sets are considered. The slope of the frequency distribution is evaluated over a restricted magnitude range; the results are very robust and independent from the magnitude range used. From the mb magnitude data we obtain region b values in the range 0.4<b<1.22, with worldwide average value b=0.87; these results are confirmed by the analysis of the seismic moment data. The steepest frequency distribution is observed in the Tonga Islands region (b=1.22); although ~60% of the worldwide deep seismicity occurs here, only few events since 1977 had seismic moment exceeding 1019 N m. The high fractal dimension (D=2.4) implies a volume partially filled with fault planes, in agreement with observations on the seismic morphology of the region. At the other extreme, South America is characterized by the largest recorded deep events and an almost complete absence of small ones (b=0.4). ¿ American Geophysical Union 1988