### Abstract:

The cumulative graphs of the probability distribution for duration of the activations (eruptions) at Klyuchevskoy and Karymsky volcanoes obey a power law. The graphs are approximated by two straight-line segments. At small and medium durations (from 1 day to 6 and 2 months) the tangent of slope angle of the repeatability graphs γ = 0.53–0.55 (γ < 1). 3) At more long activation duration, γ sharply increases by 1.6 -3 times, which probably indicates the presence of some ultimate eruption size for a given volcano or a gradual approach to such a size. An avalanche-like mechanism of magma accumulation when large floating magma-filed cracks absorb smaller overlying cracks in a permeable zone of the lithosphere is proposed. This may drastically change the law of their distribution in size from the initial exponential or normal to the power law one. Interestingly, the distribution of Volcanic Explosivity Index (VEI) for the Kamchatka volcanoes, on the one hand, and the seismic moment (M0) of strong earthquakes in Kamchatka, on the other hand, obey an exponential law with similar indexes of –γ = – 0.7 and –0.6, respectively. The frequency of occurrence of volcanic eruptions in Kamchatka in the range VEI = 2 – 5 is about 10% of the global one, which is quite a lot, since the length of the volcanic arc of Kamchatka is only about 2% of the sum of the lengths of all the volcanic arcs on Earth. The distribution of the ejected tephra (VT) for the eruptions of the volcanoes of the world and Kamchatka obeys the power law with close indexes of –γ = – (0.7–0.75). In consumption of steady state volcanism the average intervals of occurrence of eruptions in Kamchatka is estimated as follows: every 15 years (VEI = 4), every 90 years (VEI = 5), every 350 years (VEI = 6, extrapolation) and every 1,400 years (VEI = 7, extrapolation).