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Likelihood-based inference for power distributions

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Abstract

This paper considers likelihood-based inference for the family of power distributions. Widely applicable results are presented which can be used to conduct inference for all three parameters of the general location-scale extension of the family. More specific results are given for the special case of the power normal model. The analysis of a large data set, formed from density measurements for a certain type of pollen, illustrates the application of the family and the results for likelihood-based inference. Throughout, comparisons are made with analogous results for the direct parametrisation of the skew-normal distribution.

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Acknowledgements

We are most grateful to two anonymous referees for their careful reading of a previous draft of the paper and constructive suggestions towards improving it. Financial support for the research which led to the production of this paper was received from the: Spanish Ministry of Science and Education grant MTM2009-07302 and Junta de Extremadura grant PRI08A094 (Pewsey); FONDECYT grant 1090411 (Gómez); CNPq-Brasil (Bolfarine).

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Authors and Affiliations

  1. Department of Mathematics, Escuela Politécnica, University of Extremadura, Avenida de la Universidad s/n, 10003, Cáceres, Spain

    Arthur Pewsey

  2. Mathematics Department, Faculty of Basic Sciences, University of Antofagasta, Antofagasta, Chile

    Héctor W. Gómez

  3. Statistics Department, IME, University of Sao Paulo, Sao Paulo, Brazil

    Heleno Bolfarine

Authors
  1. Arthur Pewsey
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  2. Héctor W. Gómez
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  3. Heleno Bolfarine
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Correspondence to Arthur Pewsey.

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Communicated by Domingo Morales.

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Pewsey, A., Gómez, H.W. & Bolfarine, H. Likelihood-based inference for power distributions. TEST 21, 775–789 (2012). https://doi.org/10.1007/s11749-011-0280-0

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  • DOI: https://doi.org/10.1007/s11749-011-0280-0

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