On 7 February at 14:15 Annika Krutto will defend her doctral thesis "Empirical Cumulant Function Based Estimation in Stable Laws“.
prof T. Kollo, University of Tartu
Prof A. Malyarenko, Mälardalen University
Prof O. Januškevičiene, Vilnius University
In diverse fields of business, science, and engineering there is a need for modelling asymmetric data with extremes. The classical normal distribution is not suitable in such cases and alternative approaches should be used. Stable distributions, with normal distribution as a special case, can capture the fuzzy dynamics and large fluctuations that result from symmetric and asymmetric stochastic processes. However, a challenging problem in applying stable distributions to practical problems is the estimation of their parameters from the empirical data. To address this problem, in thesis a class of closed-form estimators is studied. The estimation procedure is simple but estimators depend on arbitrary selection of the number of arguments. Different selections of arguments yield different estimates thus making the method not very useful in practice. In thesis an improved version of the estimation method is provided and, based on empirical and theoretical results, suggestions on the selection of arguments are given. As the result of this dissertation it is found that the proposed computationally simple procedure for estimating the parameters of stable laws compares favourably with the more complicated algorithmic methods and can be successfully used in practice.