Table 2 Essential factors of moment expressions.
\({{{\mathrm{E}}}}(\hat D_w^2)\) | \({{{\mathrm{E}}}}(\hat D_b^2)\) | \({{{\mathrm{E}}}}(\hat D_w\hat D_b)\) | \({{{\mathrm{E}}}}(\hat D^2)\) | \({{{\mathrm{E}}}}({{{\hat{\mathrm \Delta }}}}^2)\) | \({{{\mathrm{E}}}}\left( {\hat Q} \right)\) | \({{{\mathrm{E}}}}\left( {\hat R} \right)\) | Divisor | |
|---|---|---|---|---|---|---|---|---|
\({{{\Phi }}_1}{{\Theta }}_1\) | \(n^2v^2 \times \) \((2 + vv_2)\) | \(\lambda _7\) | \( - nv \times \) \((vv_1 + \lambda _1)\) | \(v_1^2\lambda _5\) | \(2v^2n_1^2v_1^2\) | \(2v_1^2\) | \(2v^2n_1^2v_1^2\) | \(n^3v^3v_1{{{\mathrm{/}}}}Q\) |
\({{{\Phi }}_2}{{\Theta }}_2\) | \(n^2v^2\) | \(2\) | \( - nv\) | \(\lambda _5\) | \(v^2\lambda _2\) | \(2\) | \(2v^2\) | \(n^3v^2{{{\mathrm{/}}}}n_1Q\) |
\({{\Gamma }}_1\) | \( - 2n^2v^2\) | \( - 2\lambda _1\) | \(nv(1 + \lambda _4)\) | \( - 2v_1\lambda _3\) | \(2v^2v_1\lambda _2\) | \(4v_1\) | \(4v^2v_1\) | \(n^3v^2{{{\mathrm{/}}}}n_1Q\) |
\({{\Gamma }}_2\) | \(0\) | \( - 2\lambda _1\) | \( - nvv_2\) | \( - 2v_1\lambda _3\) | \( - 4v^2n_1v_1\) | \(4v_1\) | \( - 4v^2n_1v_1\) | \(n^3v^2/2n_1Q\) |
\({{\Gamma }}_3\) | \(0\) | \(4\) | \( - nv\) | \( - 2\lambda _3\) | \( - 2v^2n_2\) | \(4\) | \(4v^2\) | \(n^3v/n_1n_2Q\) |
\({{\Gamma }}_4\) | \( - 2n^2v^2v_2\) | \(2\lambda _1\lambda _4\) | \(\lambda _6\) | \( - 2v_1^2\lambda _3\) | \(4v^2n_1^2v_1^2\) | \(4v_1^2\) | \(4v^2n_1^2v_1^2\) | \(n^3v^3v_1/v_2Q\) |
\({{\Delta }}_1\) | \(n^2v^2\) | \(\lambda _7\) | \( - nv\lambda _4\) | \(2v_1^2\) | \(v^2v_1^2\lambda _2\) | \(2v_1^2\) | \(2v^2v_1^2\) | \(n^3v^2/n_1Q\) |
\({{\Delta }}_2\) | \(0\) | \(1\) | \(0\) | \(1\) | \(v^2\) | \(1\) | \(v^2n_1^2\) | \(n^3v^2/n_1v_1^2Q\) |
\({{\Delta }}_3\) | \(0\) | \( - 2\lambda _1\) | \(nv\) | \(4v_1\) | \( - 2v^2n_2v_1\) | \(4v_1\) | \(4v^2v_1\) | \(n^3v/n_1n_2Q\) |
\({{\Delta }}_4\) | \(0\) | \(v_1\) | \(0\) | \(v_1\) | \(v^2v_1\) | \(v_1\) | \( - v^2n_1v_1\) | \(n^3v/2n_1n_2Q\) |
\({{\Delta }}_5\) | \(0\) | \(1\) | \(0\) | \(1\) | \(v^2\) | \(1\) | \(v^2\) | \(n^3/n_1n_2n_3Q\) |
\({{\Delta }}_6\) | \(n^2v^2\) | \(\lambda _4^2\) | \( - nv\lambda _4\) | \(v_1^2\) | \(v^2n_1^2v_1^2\) | \(v_1^2\) | \(v^2n_1^2v_1^2\) | \(n^3v^3v_1/v_2v_3Q\) |
\({{\Delta }}_7\) | \(0\) | \( - 2\lambda _4\) | \(nv\) | \(2v_1\) | \( - 2v^2n_1v_1\) | \(2v_1\) | \( - 2v^2n_1v_1\) | \(n^3v^2/2n_1v_2Q\) |
