Conveners
Applied Statistical Methods
- Tomáš Hobza (FJFI CVUT)
A fractal dimension is a non-integer characteristic that measures the space filling of an arbitrary set. The conventional grid based methods usually provide a biased estimation of the fractal dimension, and therefore it is necessary to develop more complex methods for its estimation. A new characteristic based on the Parzen estimate formula is presented here as the modified Renyi entropy...
We derive a new distribution using maximum Renyi entropy principle under the absolute moment constraints. The newly derived distribution has four parameters: two shape parameters and location and scale parameters. The density of this distribution is smooth and twice differentiable which allows its parameters to be estimated by maximum likelihood estimation method. It is clear from its density...
The contribution presents the statistical properties of the diffusion process over fractal sets represented as sparse grids. The summary of differences between regular and sparse grid diffusion is presented together with an overview of dimension estimation methods. The main focus is on less than one-dimensional sets which allow for the analytical study of return probability. Oscillatory...
