This thesis has the intent to give an overview about the statistical methods and techniques, which can be used to describe and characterize univariate return distributions statistically, i.e. to summarize a lot of information of the distribution in one number. For example, what is the average of the observated values? How much do the observated values vary from the average? How does the assumed distribution may look like? For that, measures of the shape, i.e. measures of central tendency, of statistical dispersion and of skewness and kurtosis will be introduced. Given a sample of observations, the aim is to ????t this data with a model, particularly with a known distribution. For that, parametric distribution, will be introduced to ????t a distribution to the return data, which represents the data set of returns at the best. It may then be compared with the properties and characteristics of a normal distribution to see, if the data is normally distributed or not. One interesting assumption about the return distributions is the assumption that the sample is normally distributed. But are the observations really normally distributed? Is the assumption right? To test the hypothesis, if a data set is normally distributed, some well known statistical tests for normality will then be discussed, especially the Lilliefors Test, that is similar to the Kolmogorov test, the Jarque and Bera test based on skewness and kurtosis of a distribution and the Shapiro-Wilk test. As an alternative of the assumption, that a sample is normally distributed, is to consider a Student-t distribution.     «

This thesis has the intent to give an overview about the statistical methods and techniques, which can be used to describe and characterize univariate return distributions statistically, i.e. to summarize a lot of information of the distribution in one number. For example, what is the average of the observated values? How much do the observated values vary from the average? How does the assumed distribution may look like? For that, measures of the shape, i.e. measures of central tendency, of sta...     »