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Skewing Around: Relationships Among Classes of Skewed Distributions

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  • Barry C. Arnold

    (University of California)

  • Robert J. Beaver

    (University of California)

Abstract

The relationships among normal hidden truncation models, closed skew normal families, fundamental skew normal families and extended skew normal families are explored. The models of Arnold and Beaver in (Test 11(1):7–54, 2002) include all of these absolutely continuous models. Slightly more general absolutely continuous models are available with the label of selection models in Arellano-Valle and Genton (Journal of Multivariate Analysis 96:93–116, 2005). The hidden truncation paradigm provides a convenient description of models that subsumes the full spectrum of these skewed models, including singular and absolutely continuous versions.

Suggested Citation

  • Barry C. Arnold & Robert J. Beaver, 2007. "Skewing Around: Relationships Among Classes of Skewed Distributions," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 153-162, June.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:2:d:10.1007_s11009-007-9028-4
    DOI: 10.1007/s11009-007-9028-4
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    References listed on IDEAS

    as
    1. Loperfido, Nicola, 2002. "Statistical implications of selectively reported inferential results," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 13-22, January.
    2. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
    3. Adelchi Azzalini & Monica Chiogna, 2004. "Some results on the stress–strength model for skew-normal variates," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 315-326.
    4. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    6. Corrado Crocetta & Nicola Loperfido, 2003. "Sampling Distribution of the Gini Index from a Skew Normal," Quaderni DSEMS 07-2003, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    7. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    8. Corrado Crocetta & Nicola Loperfido, 2005. "The exact sampling distribution of L-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 213-223.
    9. Tetsuhisa Miwa & A. J. Hayter & Satoshi Kuriki, 2003. "The evaluation of general non‐centred orthant probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 223-234, February.
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    Hidden truncation; Skew-normal families;

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