  The two-parameter Poisson--Dirichlet distribution is a probability
distribution on the totality of positive decreasing sequences with sum 1 and
hence considered to govern masses of a random discrete distribution. A
characterization of the associated point process (that is, the random point
process obtained by regarding the masses as points in the positive real line)
is given in terms of the correlation functions. Using this, we apply the theory
of point processes to reveal the mathematical structure of the two-parameter
Poisson--Dirichlet distribution. Also, developing the Laplace transform
approach due to Pitman and Yor, we are able to extend several results
previously known for the one-parameter case. The Markov--Krein identity for the
generalized Dirichlet process is discussed from the point of view of functional
analysis based on the two-parameter Poisson--Dirichlet distribution.
