# Kriging

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The Kriging weights w_i1,w_i2,w_i3,…w_ik can be used to estimate the fair value of VA contracts x ⃑_i by the following formula, y ̂_i=∑_(j=1)^k▒〖w_ij∙y_j 〗. The kriging weights can be calculated by the following linear equations, Where the is a control variable, which is used to make sure that ∑_(j=1)^k▒w_ij =1. V_rs=α+exp⁡(-3/β D(z ⃑_r,z ⃑_s,λ)),r,s=1,2,3,…,k, D_ij=α+exp⁡(-3/β D(x ⃑_i,z ⃑_j,λ)),j=1,2,3,…,k, The D(.) function is the distance function mentioned in the clustering section,α≥0 and β≥0 are two parameters. The above linear equation system has a unique solution because D(z ⃑_r,z ⃑_s,λ)>0 for all r,s=1,2,3,…,k,. Then the fair value of whole portfolio X=(x ⃑_1,x ⃑_2,x ⃑_3,…,x ⃑_n)can be estimated by the following formula,…

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management factor (dimensionless) and P is the supporting practice factor (dimensionless). The factors were derived from the database. The vector-based information is converted into 10x10 m grid using the Arcview. 3. Results and discussion Rainfall-runoff (R) factor for the basin was used a single value (R=41.89), obtained from USLE trials in Soil and Water Resources Research Institute carried out throughout 1973-1982 (Ayday, 1995). Soil and land use map also were digitized in a GIS…

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