抄録
Based on a curved exponential family, there is a regularity condition that
the score function with random variables is the linear independence, which is commonly
used in the information geometry. An equivalence relation to the regularity condition
is that the Fisher information is positive definite under the curved exponential family.
We investigate a key condition for two regularity conditions and we recognize it as the
linear independence for the first derivative of natural parameter with respect to the
parameter.
