Title: On the linear combination of chi-squares with applications to inference in shape and directional statistics
Authors: Alfred Kume - University of Kent (United Kingdom) [presenting]
Andrew Wood - The University of Nottingham (United Kingdom)
Tomonari Sei - University of tokyo (Japan)
Abstract: Some random matrix models adopted for statistical analysis of directions and shapes, rely on certain relationships with the linear combination of central and non-central chi-square random variables. Motivated initially from the directional statistics problems, we focus on the density function of such distributions and not on their cumulative distribution function which have been extensively covered in the literature. Our approach provides new insight by generating alternative characterisations of the relevant expressions for a range of distributions used in directional and shape inference. In addition, our results can be easily extended to some general expectations used for spike models used in random matrix theory. The expressions we obtain are more transparent for modelling purposes and with apparent stability in their numerical evaluation. We will illustrate our method with some examples.