Document Type
Thesis
Degree
Master of Science (MS)
Department
Statistics
Advisor's Name
Jie Mi
Advisor's Title
Committee Chair
Advisor's Name
Kai Huang
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.
Recommended Citation
Shi, Yipin, "Study on Bivariate Normal Distribution" (2012). FIU Electronic Theses and Dissertations. Paper 745.
http://digitalcommons.fiu.edu/etd/745