  Consider two forms of sampling from a population: (i) drawing $s$ samples of
$n$ elements with replacement and (ii) drawing a single sample of $ns$
elements. In this paper, under the setting where the descending order
population frequency follows the Poisson--Dirichlet distribution with parameter
$\theta$, we report that the magnitude relation of the Fisher information,
which sample partitions converted from samples (i) and (ii) possess, can change
depending on the parameters, $n$, $s$, and $\theta$. Roughly speaking, if
$\theta$ is small relative to $n$ and $s$, the Fisher information of (i) is
larger than that of (ii); on the contrary, if $\theta$ is large relative to $n$
and $s$, the Fisher information of (ii) is larger than that of (i). The result
represents one aspect of random distributions.
