Energy spectrum of cosmic rays (CR) exhibits power-like behavior with very characteristic knee structure. We consider a generalized statistical model for the production process of cosmic rays which accounts for such behavior in a natural way either by assuming existence of temperature fluctuations in the source of CR, or by assuming specific temperature distribution of CR sources. Both possibilities yield the so called Tsallis statistics and lead to the power-like distribution. We argue that the knee structure arises as result of abrupt change of fluctuations in the source of CR. Its possible origin is briefly discussed.
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