Pure premium calculation of rice farm insurance scheme in Indonesia based on the 4-parameter beta mixture distribution

Abstract

The Indonesian Government introduced rice farm insurance scheme (Asuransi Usaha Tani Padi – AUTP program) to protect rice farm from loss caused by flood, drought and pest and disease infestations. It has been discussed the method to calculate pure premium of the rice farm insurance scheme in Indonesia with assume that the distribution of rice yield data is normal distribution, gamma distribution, or normal mixture distribution. The normal distribution can be used for the case of distribution of rice yield data in the form of symmetry. The gamma distribution can be used for the case of distribution of rice yield data in the form of skewed to the right or positively skewed. In addition, the normal and gamma distributions are categorized as unimodal distributions. It has also been discussed the method of calculating pure premium of the rice farm insurance scheme in Indonesia with the assumption that the rice yield data is normal mixture distribution. The normal mixture distribution can be categorized as multimodal distribution. Characteristic of the normal mixture distribution is suitable for rice yield data in Indonesia that contain rice yield data from several provinces. On the other hand, it is also known that the 4-parameter beta mixture distribution can be applied to rice yield data in Indonesia. This distribution is more flexible than the normal mixture distribution in terms of the tail shape of the distribution. In this paper, pure premium calculation method of the AUTP program is formulated with assume that the distribution of rice yield data is the 4-parameter beta mixture distribution. Monte Carlo simulation is used to evaluate performance of the method. The method is applied to the rice productivity data in several provinces in Indonesia for the period 1970 to 2016.