Research On The Record Simulation Algorithm Of Beta Random Variables

The study of record values is popular in many areas because of its wide ap-plicability in the modeling and analysis of lifetime data.Simulation studies are an integral part of statistical research.As everyone knows,simulation is used ad-vantageously in a number of situations.For example,it can provid the empirical estimation of sampling distributions,study the misspecification of assumptions in statistical procedures,determin the power in hypothesis tests,and many others.In order to design simulation studies relating to record values,one must be able to efficiently generate record samples from a wide variety of distributions.The direct algorithm is to generate a large number of distributed values through the cycle of comparison,given this condition,the workload is large and need to consume a lot of time,generating moderately large samples of record values or a large number of samples of record values will take a significant amount of time in this case and the efficiency is quite low.The purpose of this paper is to study the statistical inference method based on the rejection method,including the parameter estimation of the sample based on the record value and the prediction of the future record value.In the first chap-ter,this paper mainly introduces research background and research status of record values and simulation of different distribution,and introduce the properties of record values of classical distribution and its generation algorithm,at the same time,the specific definitions of record values,record time and Beta distribution are given which in this paper we will study;the second chapter mainly introduced the corresponding simulation algorithm in the choice of different parameters,using the rejection method to generate Beta record values,and the corresponding proof theorys are given;the third chapter.we give the simulation of record values under different algorithms which we introduced in the second chapter by the computer program R language,and we also give the corresponding test with the theoretical value,and the visualization comparison and the whole sample mean value esti-mation;Finally,we propose the deficiencies of the above models and what can be further discussed in the future.