Goodness-of-fit for a concentrated von Mises-Fisher distribution.
Goodness-of-fit for a concentrated von Mises-Fisher distribution.
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Date
2012
Authors
Adelaide Figueiredo
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Abstract
The von Mises-Fisher distribution is widely used for modelling directional
data. In this paper we propose goodness-of-fit methods for a concentrated von
Mises-Fisher distribution and we analyse by simulation some questions concerning
the application of these tests. We analyse the empirical power of the Kolmogorov-
Smirnov test for several dimensions of the sphere, supposing as alternative hypothesis
a mixture of two von Mises-Fisher distributions with known parameters.We also compare
the empirical power of the Kolmogorov-Smirnov test with the Rao's score test for
data on the sphere, supposing as alternative hypothesis, a mixture of two Fisher distributions
with unknown parameters replaced by their maximum likelihood estimates
or a 5-parameter Fisher-Bingham distribution. Finally, we give an example with real
spherical data.