| Popis: |
This thesis deals with the average absolute deviation and its use for the estimation of the standard deviation. First, the important notions are defined, in particular the mean absolute deviation and the average absolute deviation. Relationships between the standard deviation and the mean absolute deviation are derived for four probability dis- tributions, namely for the normal, exponential, Laplace distribution and for a mixture of two normal distributions. The asymptotic distribution of the average absolute deviation is derived. Subsequently, the estimation of the standard deviation via the average ab- solute deviation is considered and its asymptotic distribution is shown. Detailed results are provided for the normal and Laplace distribution. Some of the theoretical results are illustrated by simulations. In addition, the estimator of the standard deviation construc- ted using the average absolute deviation is compared to the sample standard deviation in a simulation study. 1 |
