Study On Statistical Properties Of (a,b) Distribution

Since the Chinese economic reform to the 1980 s,the first insurance company established.Insurance industry rapid development,now of the insurance industry has covered basic necessities of life.AIG(American International Group,Inc.)is a leading global insurance organizations,AIG raised four elements,which including: cost control and underwriting profit;profit pattern;inclusive of multi-culture;the investment structure,which is fundamental to insurance company.The importance of profits that AIG underwriting profit as the first highlighted terms of claims.For different categories of underwriting profit,the estimate of the loss ratio is an important factor of influence which is planted pricing and corporate profits.The claim number and claim amount are the key of factors in rating,the paper based on the research of the claim number on deeper exploration.In general,the commonly used methods for describing the distribution of losses are geometric distribution,binomial distribution,negative binomial distribution,Poisson distribution and normal distribution.The methods of obtaining the loss distribution are classical statistical method,stochastic simulation method and Bayes method.In practical applications,the insurance industry uses a number of special non-negative random variables to describe the number of losses,the number of such special loss is not a general loss of distribution,so for different data samples to determine the different losses Distribution is particularly critical.According this idea,this paper consider(a,b)distribution.we used Bayesian method to analyse a class of(a,b)distribution and to study the relationship between variance and expectation to obtain the moments estimate and maximum likelihood estimate of a and b.Base on the MLE and Lindley lemma,we study the Bayesian estimation of the classes distribution(a,b,0)and give the simulations with Matlab.From the results of simulation,we conclude that: It is better to use the Bayesian estimation method unless the sample size is small.