Integral inference method for multivariate normal distributions

A integral inference method for multivariate normal distributions is presented. Combining the simulation results and the experiment data, it can totally infer the experiment data of the multivariate normal distributions in multi-state. Then it can establish the estimators of means and covariance matrix of the multivariate normal distribution, and estimate their confidence limits and intervals in each state. Compared with traditional methods, this method not only has higher precision but also solves the problem of reliability assessment with only one experiment datum of the multivariate normal distribution in a state. Besides, a method for testing simulation results of means and variances in multi-state is also presented with very small sample.