Table 6 Transition matrix for the nephew case
From: Improved computations for relationship inference using low-coverage sequencing data
j | s | \(\sum _{k=1}^{n_j}T_i(v_{jk},v_s)\) |
|---|---|---|
1 | 1 | \((1-p)^5 + p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + p^4(1-p) + p^5\) |
1 | 2 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
1 | 3 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
1 | 4 | \(4p^2(1-p)^3 + 4p^3(1-p)^2\) |
2 | 1 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
2 | 2 | \((1-p)^5 + 2p^2(1-p)^3 + 4p^3(1-p)^2 + p^4(1-p)\) |
2 | 3 | \(p(1-p)^4 + 4p^2(1-p)^3 + 2p^3(1-p)^2 + p^5\) |
2 | 4 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
3 | 1 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
3 | 2 | \(p(1-p)^4 + 4p^2(1-p)^3 + 2p^3(1-p)^2 + p^5\) |
3 | 3 | \((1-p)^5 + 2p^2(1-p)^3 + 4p^3(1-p)^2 + p^4(1-p)\) |
3 | 4 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
4 | 1 | \(4p^2(1-p)^3 + 4p^3(1-p)^2\) |
4 | 2 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
4 | 3 | \(2p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + 2p^4(1-p)\) |
4 | 4 | \((1-p)^5 + p(1-p)^4 + 2p^2(1-p)^3 + 2p^3(1-p)^2 + p^4(1-p) + p^5\) |