Erik Bølviken: Fitting distributions when the parameters are unimportant: an actuarial viewpoint.
The talk is elementary and discusses empirical modelling of single variables with insurance losses as example. There are in such cases little or no theory to go on, and the amount of data is many situation quite scarce. Why do we so often limit ourselves to fit two-parameter families? It will be suggested that it may be a good idea to work with more flexible models with three or four parameters and that this may provide a nice framework for automating the entire procedure for the computer to work alone. Sure, with little data the parameters may be unstably estimated, but that may not apply equally to the distributions they define. Many-parameter families suitable for insurance losses will be reviewed with some simple asymptotics in an example allowing this and with Monte Carlo to throw light on the issue in other cases.
Erik Bølviken is Professor Emeritus at the Department of Mathematics, University of Oslo. Prior to this he was Associate Professor of Statistics from 1984 and Professor of Statistics from 1989 up to 2018 at the same department. He had a special responsibility for the education in insurance mathematics at the department from 1999. He is the author of the textbook Computation and Modelling in Insurance and Finance, Cambridge University Press, 2014.