On optimal tests for isotropy against the symmetric wrapped stable - circular uniform mixture family
by
Ashis SenGupta
Applied Statistics Unit, Indian Statistical Institute, Calcutta, India
Coauthors: Chandranath Pal (Department of Statistics, University of Kalyani, India)

The family of Symmetric Wrapped Stable distributions is now-a-days being widely used for modeling circular data. Mixtures of Circular Uniform with the former have also applications as a larger family of circular distributions to incorporate possible outliers. Restricting to such a mixture, we derive the locally most powerful invariant (LMPI) test for the hypothesis of isotropy or randomness of directions - expressed in terms of the null value of the mixing proportion p in the model. Global monotonicity of the power function of the test is established. The test is also consistent. Power values of the test for some selected parameter combinations, obtained through simulation, reveal quite encouraging performances even for moderate sample sizes. The P³ approach (SenGupta, 1991; Pal and SenGupta, 1998) for unknown p and \rho and the non-regular case of unknown a, the index parameter, are also discussed. Two real-life examples are presented to illustrate the inadequacy of circular normal distribution as a circular model. These are also used to demonstrate the application of the LMPI test, optimal P³ test and a Davies-motivated test. Finally a goodness-of-fit test performed on these two data sets, establishes the plausibility of the above SWS-CU mixture model for real-life data sets encountered in practical situations.

Date received: October 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafr-72.