The Application Of Mathematical Statistics In Non-life Actuarial

Actuarial science originated first in the premium calculation of life insurance business. Until well into the 20th century, with the growing number of non-life actuarial issues facing the field of non-life insurance actuarial theory was gradually developed. To the 1970s, non-life actuarial science has evolved into a separate branch. However, non-life actuarial calculation of technical maturity and completeness of the scientific theory behind the life insurance or actuarial, which is due to random factors involved in more non-life actuarial calculation error larger, quantitative analysis more difficult To solve these problems, it is necessary to a better understanding of the relevant knowledge of mathematical statistics. Only flexible use of a variety of mathematical statistics theory and methods in order to solve a variety of non-life actuarial problems encountered in practical work.This article outlines in the preface of the non-life actuarial background knowledge and basic development situation in our country, describing current mainstream non-life actuarial research and important research results, emphasizing the mathematical statistics in the study on the basis of non-life position.From the second chapter to the fourth chapter describes in detail the process of quantifying the loss of no n-life insurance. Loss as the core non-life research, combined with mathematical statistics on the basis of knowledge of random variables, the study focused on the formation of non-life actuarial losses in distribution. In the course of study the nature of the loss distribution, the use of the basic method of mathematical statistics, such as stochastic simulation, parameter estimation, hypothesis testing and so on. You can conduct a detailed analysis of the various properties of the loss distribution, and ultimately achieve precise quantification of loss. In the fifth chapter of this paper, we sort out the link between non-life actuarial premiums generated and Bayesian methods in mathematical statistics. Expounding the theory of reliability which is a new premium estimation theory originated in Bayesian methods, in the last chapter of this paper, we use the knowledge of mathematical statistics and statistical software to analyze the data for actual losses, further validated by mathematical statistics method to study the non-life actuarial reliability and accuracy.