Although many of the topics considered in STAT354, Distribution Theory and Statistical Inference, sound the same as those in the second year unit, a more theoretical approach is used, and a deeper level of understanding is required. The unit concentrates on the fundamental aspects of statistics, rather on the particular methods in use in various disciplines. To gain most benefit from studying this unit, you should read more widely in the prescribed text and other texts than the minimum indicated in the Study Guide.
The subject of statistics is concerned with summarizing the data to understand the evidence contained in the data. The topics in this unit are foundations for statistical strategies of interpreting data.
There are two (or more) schools of statistical thought. The traditional parametric statistics relies upon weak assumptions that the data can be approximated by a parametric distribution. In this way the essential information is contained in a small set of parameters. The other way is to make very few assumptions and let the data themselves decide the distribution. Whilst this may seem appealing, we could have difficulty in reducing the data to be able to interpret. Both schools have their advantages, disadvantages and adherents but most statisticians use whatever will do the job; often a blend of both.
This course is predominantly about parametric statistics with one section on non-parametric statistics, Order Statistics.
At times, distribution theory and inference seem remote from the practical problems of analysing data but progress in statistics necessitates a firm foundation in inference. As statisticians, you will be challenged with the non-standard problems where your insight into the problems may be the most important factor in success. The insight is honed by studying the theoretical bases of statistics.