Authorised by Academic Registrar, April 1996
Objectives The specific objectives of the subject GAS2631 are for students to apply techniques based on the probability density function, cumulative distribution function and moment generating function to obtain desired properties of distributions of random variables; derive the sampling distributions of summary statistics including the sample mean, sample variance and order statistics; evaluate the performance of competing point estimators in terms of bias, variance, mean square error, efficiency and consistency; apply the methods of moments and maximum likelihood to construct point estimators; compare the performance of alternative hypothesis testing procedures in terms of power; construct hypothesis tests using the likelihood ratio test principle; apply a range of standard tests to analysis of data.
Synopsis The subject is divided into two sections of approximately equal weight. Section A - Statistical distributions: univariate distributions (review of basic concepts, moments, use of moment generating functions in distribution theory, standard distributions useful in statistical analysis); multivariate distributions: joint and conditional distributions; sampling distributions of sample statistics including sample moments and order statistics. Section B - Techniques of inferential statistics: parameter estimation (criteria and methodology of point and interval estimation); parametric hypothesis testing (basic concepts, likelihood ratio tests, simple applications, including the chi-squared goodness-of-fit test); brief introduction to non-parametric methods.
Assessment Assignments: 40% + Examination (3 hours): 60%