Based on the distance of Kullback-Leibler

this paper give the exact definition of the maximum Kullback-Leibler distance between two different distribution functions and prove that this one has analytic properties such as symmetry

triangle inequality which is the same as the Euclidean distance.By the definition

the maximum Kullback-Leibler distance between some conventional distributions

such as two different binomial distributions

two different normal distributions are obtianed. Farther

for multivariable distribution

this paper give the definition of the Kullback-Leibler distance

and to derive the Kullback-Leibler distance for two different matrix Γ-distribution. On the other hand

the conditions that a normal distribution approximate to a exponetial distribution is obtained under Kullback-Leibler distance.