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On location mixtures with Pólya frequency components

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  • Balabdaoui, Fadoua
  • Butucea, Cristina

Abstract

We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X0 with a certain probability. We show that if X0 admits a density that is a Pólya frequency function with E[X0]=0, then k, a1,…,ak and π1,…,πk are identifiable for any k≥1. We discuss how log-concave maximum likelihood can be used to estimate the mixed and the unknown density f0 when the latter is symmetric.

Suggested Citation

  • Balabdaoui, Fadoua & Butucea, Cristina, 2014. "On location mixtures with Pólya frequency components," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 144-149.
    • Handle: RePEc:eee:stapro:v:95:y:2014:i:c:p:144-149
    DOI: 10.1016/j.spl.2014.08.013
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    References listed on IDEAS

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    1. Christian Hennig & Tim F. Liao, 2013. "How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 309-369, May.
    2. Chang, George T. & Walther, Guenther, 2007. "Clustering with mixtures of log-concave distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6242-6251, August.
    3. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
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