Beta distribution approximation of confidence distributions and application in reliability statistics;

Making full use of knowledge in manufacturing tolerance analysis combined with the beta distribution model is introduced and applied.

Considering the step by step improvement in the related knowledge and information, a dynamic and recurring method is advocated of assessing the containment with Bayes theorem and the solution is obtained to the problem in its practical application: how to set forth a prior Beta distribution.

The 8087 s instructions are estimated with beta distribution and normal distribution separately, the whole program s execution time is approximated with normal distribution after adding instruction.

A approximate distribution fonction from large sample is also obtained.

This paper has given a calculated method of variance of the approximate distribution of the parameter estimator that is an instrumental variable in the very general structural models,and has given an example,in which true x_t value is distributed as an exaponential random variable.

The approximate distribution of Fisher s statistics for exponential sample is given.

Based on Boltzmann distribution approximation,the net energy transfer from Tm 3+ to Ho 3+ ions has been calculated.

In order to avoid that a small amount of field test information would be obliterated by a large amount of prior information,a Bayesian method with mixed Beta distribution was used.

When prior distribution of failure-rate is in form of Beta-exponential distribution,and the super-parameters are in form of uniform distribution,we get Hierarchical Bayesian Estimation of failure probability.

In this paper,when prior distribution of failure-rate is in form of Beta-exponential distribution,the Bayesian and Hierarchical Bayesian Estimation of zero-failure data.