A new approach based on Bayesian theory is proposed to determine the empirical coefficient in soil settlement calculation. Prior distribution is assumed to he uniform in [ 0.2,1.4 ]. Posterior density function is deve...A new approach based on Bayesian theory is proposed to determine the empirical coefficient in soil settlement calculation. Prior distribution is assumed to he uniform in [ 0.2,1.4 ]. Posterior density function is developed in the condition of prior distribution combined with the information of observed samples at four locations on a passenger dedicated fine. The results show that the posterior distribution of the empirical coefficient obeys Gaussian distribution. The mean value of the empirical coefficient decreases gradually with the increasing of the load on ground, and variance variation shows no regularity.展开更多
In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random varia...In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random variables X, Y with the means EX, EY （both known）, wherein the author gives two kinds of different proofs and gets the same results.展开更多
基金The National Natural Science Foundation of China (Nos.50778180 and 50808179)
文摘A new approach based on Bayesian theory is proposed to determine the empirical coefficient in soil settlement calculation. Prior distribution is assumed to he uniform in [ 0.2,1.4 ]. Posterior density function is developed in the condition of prior distribution combined with the information of observed samples at four locations on a passenger dedicated fine. The results show that the posterior distribution of the empirical coefficient obeys Gaussian distribution. The mean value of the empirical coefficient decreases gradually with the increasing of the load on ground, and variance variation shows no regularity.
文摘In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random variables X, Y with the means EX, EY （both known）, wherein the author gives two kinds of different proofs and gets the same results.
