Study on Bivariate Normal Distribution

Authors

Yipin Shi, Florida International UniversityFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

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

Keywords

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

Date of Defense

11-9-2012

Abstract

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.

Identifier

FI12112801

Recommended Citation

Shi, Yipin, "Study on Bivariate Normal Distribution" (2012). FIU Electronic Theses and Dissertations. 745.
https://digitalcommons.fiu.edu/etd/745