By applying formal asymptotic analysis, we obtain two-dimensional model system of linearly dynamic elastic “membrane” and “flexural” shells from three-dimensional equations.

On certain conditions of assumption, we build the mathematical model in imitation of distribution of population in two spaces, and according to the mathematical model we make a study of the asymptotic distribution of population in two spaces, obtain several important results, announce .

According to the hypothesis of parameters in random effect model with equilibrium design and one-way classification H0:μ=μ0,σ2α=σ2α0,σ2=σ20H1:μ≠μ0,or σ2α≠σ2α0 or σ2≠σ20,a statistical estimator to test H0 is presented by using maximum likelihood ratio method,and then the asymptotic distribution of test statistics and its rule are given.