On parameter estimation in multi-parameter distributions

  • I.J.H. Visagie Statistics Department, University of Pretoria, South Africa. DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)
Keywords: Maximum likelihood estimator, empirical characteristic function estimator, Fourier inversion, normal inverse Gaussian distribution, Meixner distribution, log-returns.


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.


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How to Cite
Visagie, I. (2018). On parameter estimation in multi-parameter distributions. Statistics, Optimization & Information Computing, 6(3), 452-467. https://doi.org/10.19139/soic.v6i3.583
Research Articles