Bayesian Inference For Binomial Distribution With Applications

This paper reviews the content of literature [1], [3], [10],[14]has systematic analysis for the nature of the binomial distribution and parameter estimation methods.As a common discrete random variable distribution, binomial distribution has extremely wide range practical applications. Although in many practical problems, the establishment of the binomial distribution model is not complicated, but the calculation is not easy. Being inspired by Bayes assumptions,we make use of the experts experience to determine a priori distribution. If we only know that the R is in(0 , 1) and other is utterly ignorant, by Bayes assumptions taking the uniform distribution in(0 , 1) as a prior distribution of R is reasonable, if there are experts information, according to experts experience giving a (relatively conservative) lower bound R L of R, 0≤R_L≤R<1and then taking the uniform distributed in ( R_L,1) as the prior distribution of R is even more appropriate and reasonable. but if experts can not according to their own experience more truly give one, then once more give a priori distribution to the super-parameters R_L,Which is more stable than ensuring the priorie distribution completely once, the nextmethod is known as multi-storey Bayes method.In this paper, the reliability of the binomial distribution Bayes estimation and multi-layer Bayes estimation were given, some of the results were compared, and an attempt to settle calculation problems of the binomial distribution , the binomial distribution in the existing knowledge of genetics textbooks lack of systematic summary and introduction. In this paper, give examples to introduce the application of the binomial distribution for the probability calculation in genetics and life insurance issues . From these examples we can see that the probability results of genetics is not just the boring figures, but it also contains an abundant wealth of ideas and content behind the figures.