67 The solutions for a and B are obtained by solving Equations(1) and(2).This does not yield simple closed form solutions. Therefore,we use the Newton-Raphson algorithm.This entails computing the observed information matrix.Some of these computations will be needed later so let's compute the entire matrix of second partial derivatives.Let p() exp(a+Bxi) and qi(a,B)=1-pi(a,B),Now, 以物 where Jn1(a,)- ∑1p(a,3)g(a,3) ∑1cp(a,3)q(a,3) ∑1xp:(a,8)qa(a,3)∑=1p(a,3)q(a,)67 The solutions for ˆα and β ˆ are obtained by solving Equations (1) and (2). This does not yield simple closed form solutions. Therefore, we use the Newton-Raphson algorithm. This entails computing the observed information matrix. Some of these computations will be needed later so let’s compute the entire matrix of second partial derivatives. Let pi(α, β) = exp(α+βxi) 1+exp(α+βxi) and qi(α, β)=1 − pi(α, β), Now, nJn(θ) = ⎡⎣ Jn1(α, β) 0 0 Jn2(µ, σ2) ⎤⎦ where Jn1(α, β) = ⎡⎣ ni=1 pi(α, β)qi(α, β) ni=1 xipi(α, β)qi(α, β) ni=1 xipi(α, β)qi(α, β) ni=1 x2i pi(α, β)qi(α, β) ⎤⎦