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The Balakrishnan skew-normal density. (English) Zbl 1309.60008
Summary: We consider a generalization of the Azzalini skew-normal distribution. We denote this distribution by \(\mathrm{SNB}_{n}(\lambda )\). Some properties of \(\mathrm{SNB}_{n}(\lambda )\) are studied. Its moment generating function is derived, and the bivariate case of \(\mathrm{SNB}_{n}(\lambda )\) is introduced. Finally, we illustrate a numerical example and we present an application for order statistics.

MSC:
60E05 Probability distributions: general theory
62E15 Exact distribution theory in statistics
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[1] Arellano-Valle RB, Gomez HW, Quintana FA (2004) A new class of skew–normal distribution. Commun. Stat Theory Methods 33(7):1465–1480 · Zbl 1134.60304 · doi:10.1081/STA-120037254
[2] Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York · Zbl 0850.62008
[3] Arnold BC, Beaver RJ (2002) Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion). Test II, 7–54 · Zbl 1033.62013
[4] Azzalini A (1985) A class of distributions with includes the normal ones. Scand J Stat 12:171–178 · Zbl 0581.62014
[5] Azzalini A (1986) Further results on a class of distribution which includes the normal ones. Statistica 46:199–208 · Zbl 0606.62013
[6] Azzalini A, Dalla-Valle A (1996) The multivarite skew-normal distribution. Biometrika 83:715–726 · Zbl 0885.62062 · doi:10.1093/biomet/83.4.715
[7] Branco M, Dey D (2001) A general class of multivariate elliptical distributions. J Multivar Anal 79:99–113 · Zbl 0992.62047 · doi:10.1006/jmva.2000.1960
[8] Ferguson TS (1996) A course in large sample theory. Chapman and Hall, London · Zbl 0871.62002
[9] Henze N (1986) A probabilistic representation of the skew-normal distribution. Scand J Stat 13:271–275 · Zbl 0648.62016
[10] Kotz S, Johnson N (1985) Orthant probability. Encyclopedia of statistics 6:521–523, Wiley New York
[11] Roberts HV (1988) Data analysis for managers with Minitab. Scientific Press, Redwood City, CA
[12] Ross SM (1991) A course in simulation. Macmillan Publishing Company, New York
[13] Steck GP (1962) Orthant probability for the equicorrelated multivariate normal distribution. Biometrika 49(3–4):433–445 · Zbl 0114.10606
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