  Probability distributions defined on the half space are known to be quite
different from those in the full space. Here, a nonextensive entropic treatment
is presented for the half space in an analytic and self-consistent way. In this
development, the ordinary first moment of the random variable X is divergent in
contrast to the case of the full space. A general (nu)-th moment of X is
considered as a constraint in the principle of maximum Tsallis entropy. The
infinite divisibility of the distribution with an arbitrary (nu) larger than
zero and convergence of its N-fold convolution to the exact Levy-stable
distribution is discussed in detail. A feature of this derivation is that the
Levy index is related to both the values of (nu) and the index of
nonextensivity.
