Abstract
In this paper, we discuss a general class of skew two-piece skew-normal distributions, denoted by GSTPSN(λ1, λ2, ρ). We derive its moment generating function and discuss some simple and interesting properties of this distribution. We then discuss the modes of these distributions and present a useful representation theorem as well. Next, we focus on a different generalization of the two-piece skew-normal distribution which is a symmetric family of distributions and discuss some of its properties. Finally, three well-known examples are used to illustrate the practical usefulness of this family of distributions.
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References
Arellano-Valle RB, Gomez HW, Quintana FA (2004) A new class of skew-normal distribution. Commun Stat Theory Meth 33: 1465–1480
Arnold BC, Beaver RJ (2002) Skew multivariate models related to hidden truncation and/or selective reporting. Test 11: 7–54
Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12: 171–178
Azzalini A (1986) Further results on a class of distributions which includes the normal ones. Statistica 46: 199–208
Azzalini A (2005) The skew-normal distribution and related multivariate families. Scand J Stat 32: 159–188
Azzalini A, Chiogna M (2004) Some results on the stress-strength model for skew normal variate. Metron LXII: 315–326
Azzalini A, Dalla Valle A (1996) The multivariate skew-normal distribution. Biometrika 83: 715–726
Balakrishnan N (2002) Discussion on Skew multivariate models related to hidden truncation and/or selective reporting by B.C. Arnold and R.J. Beaver. Test 11: 37–39
Branco M, Dey DK (2001) A general class of multivariate elliptical distribution. J Multivar Anal 79: 99–113
Cook RD, Weisberg S (1994) An introduction to regression analysis. Wiley, New York
Gupta RC, Brown N (2001) Reliability studies of skew normal distribution and its application to a strength-stress model. Commun Stat Theory Method 30: 2427–2445
Gupta RC, Gupta RD (2004) Generalized skew normal model. Test 13: 501–524
Henze NA (1986) A probabilistic representation of the skew-normal distribution. Scand J Stat 13: 271–275
Jamalizadeh A, Balakrishnan N (2008) On order statistics from bivariate skew-normal and skew-t ν distributions. J Stat Plan Inference 138: 4187–4197
Jamalizadeh A, Balakrishnan N (2009) Order statistics from trivariate normal and t ν -distributions in term of generalized skew-normal and skew-t ν distributions. J Stat Plan Inference (to appear)
Kim HJ (2005) On a class of two-piece skew-normal distributions. Statistics 39: 537–553
Kotz S, Balakrishnan N, Johnson NL (2000) Continuous multivariate distributions, vol 1, 2nd edn. Wiley, New York
Loperfido N (2001) Quadratic forms of skew-normal random vectors. Stat Probab Lett 54: 381–387
Roberts HV (1988) Data analysis for managers with minitab. Scientific Press, Redwood City
Sharafi M, Behboodian J (2008) The Balakrishnan skew-normal density. Stat Papers 49: 769–778
Wang J, Boyer J, Genton MG (2004) A skew-symmetric representation of multivariate distributions. Stat Sinica 14: 1259–1270
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Jamalizadeh, A., Arabpour, A.R. & Balakrishnan, N. A generalized skew two-piece skew-normal distribution. Stat Papers 52, 431–446 (2011). https://doi.org/10.1007/s00362-009-0240-x
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DOI: https://doi.org/10.1007/s00362-009-0240-x