Multiparametric models of random partitions. Limit distributions and statistical inference

A $d$-dimensional parametric model on the set of partitions of $n$-set is introduced and its detailed analysis for the two-dimensional case $(d=2)$ is carried out. The asymptotic behavior of the joint distribution of the numbers of blocks of even and odd sizes of a random partition is studied for $n \to \infty$, and statistical tests for the hypothesis on the uniformity of partitions against the possible alternatives are constructed.