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We investigate a two-parameter entropy introduced by Schw\"{a}mmle andTsallis and obtain its probability distribution in the canonical ensemble. Theprobability distribution is given in terms of the Lambert W-function which hasbeen used in many branches of physics, especially in fractal structures. Also,extensivity of $S_{q,q'}$ is discussed and a relationship is found to existbetween the probabilities of a composite system and its subsystems so that thetwo-parameter entropy, $S_{q,q'}$, is extensive.

Probability distribution of (Schw\"{a}mmle and Tsallis) two-parameter entropies and the Lambert W-function