Overview

In order to formulate any statement about a system, engineers need to acquire as precise a knowledge as possible about it and the environment in which it is to work. Such knowledge cannot result from pure reasoning alone, and has to rely on observation and measurement. In the telecommunications field, for instance, these measurements will allow us detect a signal, or to estimate flow volume or the quality of service. For example, the spectral analysis of an unknown signal amounts to measuring some of its statistical characteristics such as average value or covariance, etc., in order to recognize it. Similarly, during field trials, as well as during the normal life of a telecommunications network, we have to estimate traffic levels, response times and loss ratio. Again, for reliability studies, equipment lifetime, system availability, etc. are measured. Similar measurements can be made in the preliminary design step, during simulation studies.

As a consequence, a certain amount of data is collected on the system, and the question is now how to interpret them and to summarize them.

Descriptive statistics help us to choose the parameters of interest and present the results in a synthetic way that is, in visualizable form.

Now, exhaustive measurements are clearly impossible to obtain. Mathematical statistics aim at providing tools to analyze data in order to extract all the possible information from it. For instance, estimation theory intends to evaluate the confidence level to be associated with the...