Tarım Sigortalarında Konumsal Kümeleme Üzerine Bir Çalışma

Abstract

The purpose of this study is to make a fair premium estimation for wheat production. We prefer layer based clustering model where location, damage ratio and damage probability compose the layers. For the first layer, claim regions' location properties are examined. Optimal clustering results are obtained by using the spherical k-means algorithm, which is a distance-based clustering approach, and finite mixture von-Mises Fisher distribution which makes a density-based clustering. For the second layer, given the claim clusters, damage ratio values are fitted and for the third layer, given the first two layers, we model the damage probability obtained from claim data. Finite mixture of Beta distribution model is used for modelling the second and the third layers. The actuarial risk premium account is calculated by both clustering methods.

The result of the study shows that the premiums calculated by finite mixtures of von-Mises Fisher distribution and spherical k-means algorithm vary according to the locational characteristics. In addition, the change in damage ratios and probabilities can be more accurately measured by the premium using finite mixtures of von Mises Fisher distribution .

Key words: Directional Data, Spherical K-means Clustering Algorithm, Finite Mixtures of von-Mises Fisher Distribution, Finite Mixtures of Beta Distribution Model