Equation (A7) leads straight away to your optimal value of ? * appearing in Equation (8).

Equation (A7) leads straight away to your optimal value of ? * appearing in Equation (8).

The presumption of analytical liberty suggests that the joint likelihood thickness purpose of the elements of ?X? is:

(B1) f X; ? 1, ? 2, … ? m = ? i = 1 m ? i ag ag e – ? i = 1 m ? i x i (B1)

The likelihood that the discovery that is arbitrary have attributes satisfying the conditions imposed by the minimal set is:

(B2) P r o b x 1 x 1, min, …. X n x n, min = 1 – F X min = e – ? i = 1 n ? i x i, min (B2)

The numerator for the anticipated energy in Equation (4) when you look at the case that is special:

(B3) ? x n, min ? ? ? x 1, min ? U X f X d x 1 ? d x n = ? x n, min ? ? ? x 1, min ? ? i = 1 n w i x i ? i = 1 n ? i ag ag e – ? i i ? i = 1 n d x i (B3)

The independence that is statistical of random factors in X enable the phrase regarding the right-hand part of Equation (B3) to solve since:

(B4) ? x n, min ? ? ? x 1, min ? U X f X d x 1 ? d x n = ? i = 1 n ? x i, min ? w i x i ? i e – ? i x i d x i (B4)

It’s a calculation that is straightforward show that the definite integral within the summand in B4 is:

(B5) ? i that is x min ? x i ? i e – ? i x i d x i = x i, min + 1 ? Continue reading “Equation (A7) leads straight away to your optimal value of ? * appearing in Equation (8).”