**4. Fisher Information**

The Fisher information matrix of the ϕ = (β1, β2 , β3) is expressed as

$$\mathbf{I}\_{3 \times 3} = -\mathbf{E} \begin{bmatrix} \mathbf{A}\_{11} & \mathbf{A}\_{12} & \mathbf{A}\_{13} \\ \mathbf{A}\_{21} & \mathbf{A}\_{22} & \mathbf{A}\_{23} \\ \mathbf{A}\_{31} & \mathbf{A}\_{32} & \mathbf{A}\_{33} \end{bmatrix}, \tag{18}$$

where **A**11 = **E**- *∂*2 *∂*β21 , **A**12 = **A**21 = **E** *∂*2 *∂*β2*∂*β1 , **A**13 = **A**31 = **E** *∂*2 *∂*β1*∂*β3 , **A**22 = **E**- *∂*2 *∂*β22 , **A**23 = **A**32 = **E** *∂*2 *∂*β2*∂*β3 **A**33 = **E**- *∂*2 *∂*β23 , *∂*2 *∂*β21 = −m1 β21 + ln(α)∑m1 **<sup>i</sup>**=<sup>1</sup>[xi(Rxi + <sup>1</sup>)]2e−β1xi(Rxi+<sup>1</sup>), *∂*2 *∂*β2*∂*β1 = *∂*2 *∂*β1*∂*β3 = *∂*2 *∂*β2*∂*β3 = 0 *∂*2 *∂*β22 = −m2 β2 + ln(α)∑m2 **<sup>i</sup>**=<sup>1</sup>1yik2Ryi + <sup>1</sup> \*2e−β2yi(k2Ryi+<sup>1</sup>), *∂*2 =−m3 +ln(α)∑m3 **<sup>i</sup>**=<sup>1</sup>[zi(k3Rzi+<sup>1</sup>)]2e−β3zi(k3Rzi+<sup>1</sup>).
