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Testing for Normality When the Sampled Distribution Is Extended Skew-Normal

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Mathematical and Statistical Methods for Actuarial Sciences and Finance

Abstract

The extended skew-normal (ESN) distribution includes the normal one as a special case. Unfortunately, its information matrix is singular under normality, thus preventing application of standard likelihood-based methods for testing the null hypothesis of normality. The paper shows that for univariate ESN distributions the sample skewness provides the locally most powerful test for normality among the location and scale invariant ones. The generalization to multivariate ESN distributions considers projections of the data onto the direction corresponding to maximal skewness. Related computational problems simplifies for the multivariate ESN distribution, where the direction maximizing skewness is shown to have a simple parametric interpretation.

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Author information

Authors and Affiliations

  1. Facoltà di Giurisprudenza, Università degli Studi di Urbino “Carlo Bo”, Via Matteotti 1, 61029, Urbino (PU), Italy

    Cinzia Franceschini

  2. Dipartimento di Economia, Società e Politica, Università degli Studi di Urbino “Carlo Bo”, Via Saffi 42, 61029, Urbino (PU), Italy

    Nicola Loperfido

Authors
  1. Cinzia Franceschini
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  2. Nicola Loperfido
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Corresponding author

Correspondence to Nicola Loperfido .

Editor information

Editors and Affiliations

  1. Department of Economics, Ca’ Foscari University of Venice, Venice, Italy

    Marco Corazza  & Claudio Pizzi  & 

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Franceschini, C., Loperfido, N. (2014). Testing for Normality When the Sampled Distribution Is Extended Skew-Normal. In: Corazza, M., Pizzi, C. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-02499-8_15

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