Document Type



Master of Science (MS)



First Advisor's Name

Jie Mi

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Kai Huang

Third Advisor's Name

B. M. Golam Kibria


Bivariate Normal Distribution, MLE, MSE, Bias, Testing Power

Date of Defense



Let (X, Y) be bivariate normal random vectors which represent the responses as a result of Treatment 1 and Treatment 2. The statistical inference about the bivariate normal distribution parameters involving missing data with both treatment samples is considered. Assuming the correlation coefficient ρ of the bivariate population is known, the MLE of population means and variance (ξ, η, and σ2) are obtained. Inferences about these parameters are presented. Procedures of constructing confidence interval for the difference of population means ξ – η and testing hypothesis about ξ – η are established. The performances of the new estimators and testing procedure are compared numerically with the method proposed in Looney and Jones (2003) on the basis of extensive Monte Carlo simulation. Simulation studies indicate that the testing power of the method proposed in this thesis study is higher.


FI12112801 (597 kB)



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