Bayesian Prediction Base On Record Values

Record value is a random variable for a specific time. Application of record values can be seen everywhere in daily life.Such as sports records,records of meteorological rainfall records,meteorological temperature records, flood levels of the river. So it is profound practical significance to analyse record values. This paper mainly we consider Bayesian prediction base on the upper and lower recorded data, and present a subtle difference between the upper and lower record values. First, we consider record data to obey the general form of the parameter distribution model, this general distribution form include other common distributions, such as exponential distribution, Weibull distribution and so on. In the case of the prior distribution is a general form, we derive the next record value under the square loss Bayesian forecasting formula. Next, in order to prove the conclusion,we detailed derive Exponential(θ) distribution point of prediction and interval prediction under the condition of record value; on the lower record value, through different parameter settings show the Inverse Exponential(θ) distribution, Inverse Weibull(α,β) distribution point of prediction and interval prediction. Finally, we use the data simulation to verify our prediction method, and apply it to real data examples, and get a good prediction effect.