  We investigate behavior of the Fisher information matrix of general stable
distributions. DuMouchel (1975, 1983) proved that the Fisher information of
characteristic exponent \alpha diverges to infinity as \alpha approaches 2.
Nagaev and Shkol'nik (1988) made more detailed analysis and derived asymptotic
behavior of the Fisher information matrix of \alpha diverging to infinity as
\alpha approaches 2 in the symmetric case. Extending their work in this paper
we have obtained behavior of the Fisher information matrix of general stable
distributions as \alpha approaches 2 by detailed study of behavior of the
corresponding density and its score functions. We clarify the limiting values
of the 4*4 Fisher Information matrix with respect to the location \mu, the
scale \sigma, the characteristic exponent \alpha and the skewness parameter
\beta.
