New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

Study on Bivariate Normal Distribution

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.

Application of a Bivariate Probit Model to Investigate the Intended Evacuation from Hurricane

With evidence of increasing hurricane risks in Georgia Coastal Area (GCA) and Virginia in the U.S. Southeast and elsewhere, understanding intended evacuation behavior is becoming more and more important for community planners. My research investigates intended evacuation behavior due to hurricane risks, a behavioral survey of the six counties in GCA under the direction of two social scientists with extensive experience in survey research related to citizen and household response to emergencies and disasters. Respondents gave answers whether they would evacuate under both voluntary and mandatory evacuation orders. Bivariate probit models are used to investigate the subjective belief structure of whether or not the respondents are concerned about the hurricane, and the intended probability of evacuating as a function of risk perception, and a lot of demographic and socioeconomic variables (e.g., gender, military, age, length of residence, owning vehicles).

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.