Visagie, I.J.H. (Jaco)2019-08-082019-08-082018-09Visagie, I.H.J. 2018, 'On parameter estimation in multi-parameter distributions', Statistics, Optimization and Information Computing, vol. 6, pp. 452-467.2311-004X (print)2310-5070 (online)10.19139/soic.v6i3.583http://hdl.handle.net/2263/70912This research was done as part of the author’s doctoral studies under the supervision of Prof. F. Lombard. The author would like to sincerely thank Prof. Lombard for his guidance.Many-multi parameter distributions have limit cases containing fewer parameters. This paper demonstrates that, when fitting distributions to data realized from a distribution resembling one of these limit cases, the parameter estimates obtained vary wildly between estimators. Special attention is paid to the modelling of financial log-returns. Two classes of estimators are used in order to illustrate the behaviour of the parameter estimates; the maximum likelihood estimator and the empirical characteristic function estimator. This paper discusses numerical problems associated with the maximum likelihood estimator for certain distributions and proposes a solution using Fourier inversion. In addition to simulation results, parameter estimates are obtained by fitting the normal inverse Gaussian and Meixner distributions to smooth bootstrap samples from the log-returns of the Dow Jones Industrial Average index are included as examples.en© 2018 International Academic PressMaximum likelihood estimatorEmpirical characteristic function estimatorFourier inversionNormal inverse Gaussian distributionMeixner distributionLog-returnsArticle