Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 3, 440--449

Identifiability of Finite Mixtures - with Applications to Circular Distributions


Hajo Holzmann, Axel Munk and Bernd Stratmann, Georg-August-University G\"{o}tingen, Germany

SUMMARY. A general result about identifiability and strong identifiability of finite mixtures of a family of distributions is obtained via tail conditions on the corresponding characteristic functions. This is applied to location-scale families on the real line and to circular distributions. Particular cases include circular wrapped distributions of location-scale families, stable distributions and the $d$-dimensional wrapped normal distribution. Finally, counter examples are given which highlight differences between identifiability on the real line and on the circle.

AMS (1991) subject classification}. Primary 62E10; secondary 62F03, 62F05.

Key words and phrases. Circular distributions, finite mixture, wrapped distributions, identifiability, characteristic function, location-scale family, Fourier transform, stable distributions.

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