The skew-normal and related families

The Skew-Normal and Related Families

Volumn , Issue , 2011, Pages 1-262

  Capitanio, Antonella ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84922936789     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9781139248891     Document Type: Book

References (281)

1. Abe, T. and Pewsey, A. 2011. Sine-skewed circular distributions. Statist. Papers, 52, 683–707. [210]
2. Adcock, C. J. 2004. Capital asset pricing in UK stocks under the multivariate skewnormal distribution. Chap. 11, pages 191–204 of: Genton, M. G. (ed.), Skewelliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [159]
3. Adcock, C. J. 2007. Extensions of Stein’s lemma for the skew-normal distribution. Commun. Statist. Theory Methods, 36, 1661–1671. [163, 200]
4. Adcock, C. J. 2010. Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution. Ann. Oper. Res., 176, 221–234. [183, 186]
5. Adcock, C. J. and Shutes, K. 1999. Portfolio selection based on the multivariate-skew normal distribution. Pages 167–177 of: Skulimowski, A. M. J. (ed.), Financial Modelling. Kraków: Progress and Business Publishers. Available in 2001. [142, 158, 186]
6. Aigner, D. J., Lovell, C. A. K., and Schmidt, P. 1977. Formulation and estimation of stochastic frontier production function model. J. Economet., 6, 21–37. [91]
7. Aitchison, J. 1986. The Statistical Analysis of Compositional Data. London: Chapman & Hall. [210, 211]
8. Anděl, J., Netuka, I., and Zvára, K. 1984. On threshold autoregressive processes. Kybernetika, 20, 89–106. Prague: Academia. [43]
9. Arellano-Valle, R. B. 2010. The information matrix of the multivariate skew-t distribution. Metron, LXVIII, 371–386. [180]
10. Arellano-Valle, R. B. and Azzalini, A. 2006. On the unification of families of skewnormal distributions. Scand. J. Statist., 33, 561–574. [200, 201]
11. Arellano-Valle, R. B. and Azzalini, A. 2008. The centred parametrization for the multivariate skew-normal distribution. J. Multiv. Anal., 99, 1362–1382. Corrigendum: vol. 100 (2009), p. 816. [146, 149]
12. Arellano-Valle, R. B. and Azzalini, A. 2013. The centred parameterization and related quantities of the skew-t distribution. J. Multiv. Anal., 113, 73–90. Available online 12 June 2011. [114, 180]
13. Arellano-Valle, R. B. and del Pino, G. E. 2004. From symmetric to asymmetric distributions: a unified approach. Chap. 7, pages 113–130 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [14]
14. Arellano-Valle, R. B. and Genton, M. G. 2005. On fundamental skew distributions. J. Multiv. Anal., 96, 93–116. [14, 23, 200]
15. Arellano-Valle, R. B. and Genton, M. G. 2007. On the exact distribution of linear combinations of order statistics from dependent random variables. J. Multiv. Anal., 98, 1876–1894. Corrigendum: 99 (2008) 1013. [203]
16. Arellano-Valle, R. B. and Genton, M. G. 2010a. An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators. Ann. Inst. Statist. Math., 62, 363–381. [14]
17. Arellano-Valle, R. B. and Genton, M. G. 2010b. Multivariate extended skew-t distributions and related families. Metron, LXVIII, 201–234. [183, 184, 194]
18. Arellano-Valle, R. B. and Genton, M. G. 2010c. Multivariate unified skew-elliptical distributions. Chil. J. Statist., 1, 17–33. [201]
19. Arellano-Valle, R. B. and Richter, W.-D. 2012. On skewed continuous ln, p-symmetric distributions. Chil. J. Statist., 3, 195–214. [212, 213]
20. Arellano-Valle, R. B., del Pino, G., and San Martín, E. 2002. Definition and probabilistic properties of skew-distributions. Statist. Probab. Lett., 58, 111–121. [14]
21. Arellano-Valle, R. B., Gómez, H. W., and Quintana, F. A. 2004. A new class of skewnormal distributions. Commun. Statist. Theory Methods, 33, 1465–1480. [48]
22. Arellano-Valle, R. B., Bolfarine, H., and Lachos, V. H. 2005a. Skew-normal linear mixed models. J. Data Science, 3, 415–438. [94, 219]
23. Arellano-Valle, R. B., Gómez, H. W., and Quintana, F. A. 2005b. Statistical inference for a general class of asymmetric distributions. J. Statist. Plann. Inference, 128, 427–443. [22]
24. Arellano-Valle, R. B., Branco, M. D., and Genton, M. G. 2006. A unified view on skewed distributions arising from selections. Canad. J. Statist., 34, 581–601. [14, 22]
25. Arellano-Valle, R. B., Bolfarine, H., and Lachos, V. H. 2007. Bayesian inference for skew-normal linear mixed models. J. Appl. Statist., 34, 663–682. [219]
26. Arellano-Valle, R. B., Genton, M. G., and Loschi, R. H. 2009. Shape mixtures of multivariate skew-normal distributions. J. Multiv. Anal., 100, 91–101. [49]
27. Arellano-Valle, R. B., Contreras-Reyes, J. E., and Genton, M. G. 2013. Shannon entropy and mutual information for multivariate skew-elliptical distributions. Scand. J. Statist., 40, 42–62. Available online 27 February 2012 (corrected 4 April 2012). [142]
28. Arnold, B. C. and Beaver, R. J. 2000a. Hidden truncation models. Sankhyā, ser. A, 62, 22–35. [158]
29. Arnold, B. C. and Beaver, R. J. 2000b. The skew-Cauchy distribution. Statist. Probab. Lett., 49, 285–290. [190, 194]
30. Arnold, B. C. and Beaver, R. J. 2002. Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion). Test, 11, 7–54. [14]
31. Arnold, B. C. and Lin, G. D. 2004. Characterizations of the skew-normal and generalized chi distributions. Sankhyā, 66, 593–606. [50]
32. Arnold, B. C., Beaver, R. J., Groeneveld, R. A., and Meeker, W. Q. 1993. The nontruncated marginal of a truncated bivariate normal distribution. Psychometrika, 58, 471–478. [43, 87]
33. Arnold, B. C., Castillo, E., and Sarabia, J.M. 2002. Conditionally specified multivariate skewed distributions. Sankhyā, ser. A, 64, 206–226. [23]
34. Azzalini, A. 1985. A class of distributions which includes the normal ones. Scand. J. Statist., 12, 171–178. [11, 43, 71, 72]
35. Azzalini, A. 1986. Further results on a class of distributions which includes the normal ones. Statistica, XLVI, 199–208. [11, 43, 101, 116, 123]
36. Azzalini, A. 1996. Statistical Inference Based on the Likelihood. London: Chapman & Hall. [237]
37. Azzalini, A. 2001. A note on regions of given probability of the skew-normal distribution. Metron, LIX, 27–34. [161]
38. Azzalini, A. 2005. The skew-normal distribution and related multivariate families (with discussion). Scand. J. Statist., 32, 159–188 (C/R 189–200). [44]
39. Azzalini, A. 2012. Selection models under generalized symmetry settings. Ann. Inst. Statist. Math., 64, 737–750. Available online 5 March 2011. [17, 23]
40. Azzalini, A. and Arellano-Valle, R. B. 2013. Maximum penalized likelihood estimation for skew-normal and skew-t distributions. J. Statist. Plann. Inference, 143, 419–433. Available online 30 June 2012. [80, 82, 112]
41. Azzalini, A. and Bacchieri, A. 2010. A prospective combination of phase II and phase III in drug development. Metron, LXVIII, 347–369. [200, 225]
42. Azzalini, A. and Capitanio, A. 1999. Statistical applications of the multivariate skew normal distribution. J. R. Statist. Soc., ser. B, 61, 579–602. Full version of the paper at arXiv.org:0911.2093. [11, 17, 71, 141, 145, 165, 175]
43. Azzalini, A. and Capitanio, A. 2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. R. Statist. Soc., ser. B, 65, 367–389. Full version of the paper at arXiv.org:0911.2342. [11, 105, 111, 175, 178, 179, 193, 194]
44. Azzalini, A. and Chiogna, M. 2004. Some results on the stress–strength model for skew-normal variates. Metron, LXII, 315–326. [225]
45. Azzalini, A. and Dalla Valle, A. 1996. The multivariate skew-normal distribution. Biometrika, 83, 715–726. [140, 165]
46. Azzalini, A. and Genton, M. G. 2008. Robust likelihood methods based on the skew-t and related distributions. Int. Statist. Rev., 76, 106–129. [112, 116, 145]
47. Azzalini, A. and Regoli, G. 2012a. Some properties of skew-symmetric distributions. Ann. Inst. Statist. Math., 64, 857–879. Available online 9 September 2011. [11, 19, 175, 189]
48. Azzalini, A. and Regoli, G. 2012b. The work of Fernando de Helguero on nonnormality arising from selection. Chil. J. Statist., 3, 113–129. [46]
49. Azzalini, A., Dal Cappello, T., and Kotz, S. 2003. Log-skew-normal and log-skew-t distributions as model for family income data. J. Income Distrib., 11, 12–20. [54]
50. Azzalini, A., Genton, M. G., and Scarpa, B. 2010. Invariance-based estimating equations for skew-symmetric distributions. Metron, LXVIII, 275–298. [55, 206]
51. Balakrishnan, N. 2002. Comment to a paper by B. C. Arnold & R. Beaver. Test, 11, 37–39. [201, 202]
52. Balakrishnan, N. and Scarpa, B. 2012. Multivariate measures of skewness for the skewnormal distribution. J. Multiv. Anal., 104, 73–87. [141]
53. Basso, R. M., Lachos, V. H., Cabral, C. R. B., and Ghosh, P. 2010. Robust mixture modeling based on scale mixtures of skew-normal distributions. Comp. Statist. Data An., 54, 2926–2941. [221]
54. Bayes, C. L. and Branco, M. D. 2007. Bayesian inference for the skewness parameter of the scalar skew-normal distribution. Brazilian J. Probab. Stat., 21, 141–163. [83, 84]
55. Bazán, J. L., Branco, M. D., and Bolfarine, H. 2006. A skew item response model. Bayesian Anal., 1, 861–892. [227]
56. Behboodian, J., Jamalizadeh, A., and Balakrishnan, N. 2006. A new class of skew- Cauchy distributions. Statist. Probab. Lett., 76, 1488–1493. [120]
57. Berlik, S. 2006. Directed Evolutionary Algorithms. Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften, Universität Dortmund, Fachbereich Informatik, Dortmund. [218]
58. Birnbaum, Z. W. 1950. Effect of linear truncation on a multinormal population. Ann. Math. Statist., 21, 272–279. [42]
59. Bolfarine, H., Montenegro, L. C., and Lachos, V. H. 2007. Influence diagnostics for skew-normal linear mixed models. Sankhyā, 69, 648–670. [220]
60. Box, G. P. and Tiao, G. C. 1973. Bayesian Inference in Statistical Analysis. NewYork: Addison-Wesley. [95]
61. Branco, M. D. and Dey, D. K. 2001. A general class of multivariate skew-elliptical distributions. J. Multiv. Anal., 79, 99–113. [104, 175, 178]
62. Branco, M. D. and Dey, D. K. 2002. Regression model under skew elliptical error distribution. J.Math. Sci. (New Series), Delhi, 1, 151–168. [111]
63. Cabral, C. R. B., Lachos, V. H., and Prates, M. O. 2012. Multivariate mixture modeling using skew-normal independent distributions. Comp. Statist. Data An., 56, 126–142. [221]
64. Cabras, S. and Castellanos, M. E. 2009. Default Bayesian goodness-of-fit tests for the skew-normal model. J. Appl. Statist., 36, 223–232. [87]
65. Cabras, S., Racugno, W., Castellanos, M. E., and Ventura, L. 2012. A matching prior for the shape parameter of the skew-normal distribution. Scand. J. Statist., 39, 236–247. [84]
66. Callegaro, A. and Iacobelli, S. 2012. The Cox shared frailty model with log-skewnormal frailties. Statist. Model., 12, 399–418. [228]
67. Canale, A. 2011. Statistical aspects of the scalar extended skew-normal distribution. Metron, LXIX, 279–295. [55, 87]
68. Capitanio, A. 2010. On the approximation of the tail probability of the scalar skewnormal distribution. Metron, LXVIII, 299–308. [53]
69. Capitanio, A. 2012. On the canonical form of scale mixtures of skew-normal distributions. Available at arXiv.org:1207.0797. [123, 141, 175, 195]
70. Capitanio, A. and Pacillo, S. 2008. A Wald’s test for conditional independence skew normal graphs. Pages 421–428 of: Proceedings in Computational Statistics: CompStat 2008. Heidelberg: Physica-Verlag. [158]
71. Capitanio, A., Azzalini, A., and Stanghellini, E. 2003. Graphical models for skewnormal variates. Scand. J. Statist., 30, 129–144. [87, 158]
72. Cappuccio, N., Lubian, D., and Raggi, D. 2004. MCMC Bayesian estimation of a skew- GED stochastic volatility model. Studies in Nonlinear Dynamics and Econometrics, 8, Article 6. [101]
73. Carmichael, B. and Coën, A. 2013. Asset pricing with skewed-normal return. Finance Res. Letters, 10, 50–57. Available online 1 February 2013. [159]
74. Carota, C. 2010. Tests for normality in classes of skew-t alternatives. Statist. Probab. Lett., 80, 1–8. [122]
75. Chai, H. S. and Bailey, K. R. 2008. Use of log-skew-normal distribution in analysis of continuous data with a discrete component at zero. Statist. Med., 27, 3643–3655. [54]
76. Chang, C.-H., Lin, J.-J., Pal, N., and Chiang, M.-C. 2008. A note on improved approximation of the binomial distribution by the skew-normal distribution. Amer. Statist., 62, 167–170. [215]
77. Chang, S.-M. and Genton, M. G. 2007. Extreme value distributions for the skewsymmetric family of distributions. Commun. Statist. Theory Methods, 36, 1705– 1717. [53, 122]
78. Chen, J. T. and Gupta, A. K. 2005. Matrix variate skew normal distributions. Statistics, 39, 247–253. [212]
79. Chen, M.-H. 2004. Skewed link models for categorical response data. Chap. 8, pages 131–152 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [226]
80. Chen, M.-H., Dey, D. K., and Shao, Q.-M. 1999. A new skewed link model for dichotomous quantal response data. J. Amer. Statist. Assoc., 94, 1172–1186. [226]
81. Chiogna, M. 1998. Some results on the scalar skew-normal distribution. J. Ital. Statist. Soc., 7, 1–13. [43, 51, 54]
82. Chiogna, M. 2005. A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution. Stat. Meth. & Appl., 14, 331–341. [72]
83. Chu, K. K., Wang, N., Stanley, S., and Cohen, N. D. 2001. Statistical evaluation of the regulatory guidelines for use of furosemide in race horses. Biometrics, 57, 294–301. [160]
84. Churchill, E. 1946. Information given by odd moments. Ann. Math. Statist., 17, 244–246. [123]
85. Coelli, T. J., Prasada Rao, D. S., O’Donnell, C., and Battese, G. E. 2005. An Introduction to Efficiency and Productivity Analysis, 2nd edn. Berlin: Springer-Verlag. [91]
86. Contreras-Reyes, J. E. and Arellano-Valle, R. B. 2012. Kullback–Leibler divergence measure for multivariate skew-normal distributions. Entropy, 14, 1606–1626. [142]
87. Copas, J. B. and Li, H. G. 1997. Inference for non-random samples (with discussion). J. R. Statist. Soc., ser. B, 59, 55–95. [89]
88. Corns, T. R. A. and Satchell, S. E. 2007. Skew Brownian motion and pricing European options. European J. Finance, 13, 523–544. [223]
89. Corns, T. R. A. and Satchell, S. E. 2010. Modelling conditional heteroskedasticity and skewness using the skew-normal distribution one-sided coverage intervals with survey data. Metron, LXVIII, 251–263. [224]
90. Cox, D. R. 1977. Discussion of ‘Do robust estimators work with real data?’ by Stephen M. Stigler. Ann. Statist., 5, 1083. [97]
91. Cox, D. R. 2006. Principles of Statistical Inference. Cambridge: Cambridge University Press. [69]
92. Cox, D. R. and Wermuth, N. 1996. Multivariate Dependencies: Models, Analysis and Interpretation. London: Chapman & Hall. [154]
93. Cramér, H. 1946. Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press. [33, 61]
94. Dalla Valle, A. 1998. La Distribuzione Normale Asimmetrica: Problematiche e Utilizzi nelle Applicazioni. Tesi di dottorato, Dipartimento di Scienze Statistiche, Università di Padova, Padova, Italia. [56]
95. Dalla Valle, A. 2007. A test for the hypothesis of skew-normality in a population. J. Statist. Comput. Simul., 77, 63–77. [86]
96. de Helguero, F. 1909a. Sulla rappresentazione analitica delle curve abnormali. Pages 288–299 of: Castelnuovo, G. (ed.), Atti del IV Congresso Internazionale dei Matematici (Roma, 6–11 Aprile 1908), vol. III, sezione III-B. Roma: R. Accademia dei Lincei. Available at http://www.mathunion.org/ICM/ICM1908.3/Main/ icm1908.3.0288.0299.ocr.pdf. [44]
97. de Helguero, F. 1909b. Sulla rappresentazione analitica delle curve statistiche. Giornale degli Economisti, XXXVIII, serie 2, 241–265. [44]
98. De Luca, G. and Loperfido, N. M. R. 2004. A skew-in-mean GARCH model. Chap. 12, pages 205–222 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [224]
99. De Luca, G., Genton, M. G., and Loperfido, N. 2005. A multivariate skew-GARCH model. Adv. Economet., 20, 33–57. [224]
100. Dharmadhikari, S. W. and Joag-dev, K. 1988. Unimodality, Convexity, and Applications. New York: Academic Press. [19, 189]
101. DiCiccio, T. J. and Monti, A. C. 2004. Inferential aspects of the skew exponential power distribution. J. Amer. Statist. Assoc., 99, 439–450. [101]
102. DiCiccio, T. J. and Monti, A. C. 2011. Inferential aspects of the skew t-distribution. Quaderni di Statistica, 13, 1–21. [112]
103. Domínguez-Molina, J. A. and Rocha-Arteaga, A. 2007. On the infinite divisibility of some skewed symmetric distributions. Statist. Probab. Lett., 77, 644–648. [54]
104. Domínguez-Molina, J. A., González-Farías, G., and Ramos-Quiroga, R. 2004. Skewnormality in stochastic frontier analysis. Chap. 13, pages 223–242 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [225]
105. Efron, B. 1981. Nonparametric standard errors and confidence intervals (with discussion). Canad. J. Statist., 9, 139–172. [55]
106. Elal-Olivero, D., Gómez, H. W., and Quintana, F. A. 2009. Bayesian modeling using a class of bimodal skew-elliptical distributions. J. Statist. Plann. Inference, 139, 1484–1492. [213]
107. Elandt, R. C. 1961. The folded normal distribution: two methods of estimating parameters from moment. Technometrics, 3, 551–562. [52]
108. Ellison, B. E. 1964. Two theorems for inferences about the normal distribution with applications in acceptance sampling. J. Amer. Statist. Assoc., 59, 89–95. [26, 233]
109. Fang, B. Q. 2003. The skew elliptical distributions and their quadratic forms. J. Multiv. Anal., 87, 298–314. [175, 193]
110. Fang, B. Q. 2005a. Noncentral quadratic forms of the skew elliptical variables. J. Multiv. Anal., 95, 410–430. [175]
111. Fang, B. Q. 2005b. The t statistic of the skew elliptical distributions. J. Statist. Plann. Inference, 134, 140–157. [175]
112. Fang, B. Q. 2006. Sample mean, covariance and T2 statistic of the skew elliptical model. J. Multiv. Anal., 97, 1675–1690. [175]
113. Fang, B. Q. 2008. Noncentral matrix quadratic forms of the skew elliptical variables. J. Multiv. Anal., 99, 1105–1127. [175]
114. Fang, K.-T. and Zhang, Y.-T. 1990. Generalized Multivariate Analysis. Berlin: Springer Verlag. [168]
115. Fang, K.-T., Kotz, S., and Ng, K. W. 1990. Symmetric Multivariate and Related Distributions. London: Chapman & Hall. [168]
116. Fechner, G. T. 1897. Kollectivmasslehre. Leipzig: Verlag von Wilhelm Engelmann. Published posthumously, completed and edited by G. F. Lipps. [21]
117. Fernández, C. and Steel, M. F. J. 1998. On Bayesian modeling of fat tails and skewness. J. Amer. Statist. Assoc., 93, 359–371. [22]
118. Firth, D. 1993. Bias reduction of maximum likelihood estimates. Biometrika, 80, 27– 38. Amendment: vol. 82, 667. [79]
119. Flecher, C., Allard, D., and Naveau, P. 2010. Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data. Metron, LXVIII, 331–345. [52]
120. Forina, M., Armanino, C., Castino, M., and Ubigli, M. 1986. Multivariate data analysis as a discriminating method of the origin of wines. Vitis, 25, 189–201. [59]
121. Frederic, P. 2011. Modeling skew-symmetric distributions using B-spline and penalties. J. Statist. Plann. Inference, 141, 2878–2890. [204]
122. Frühwirth-Schnatter, S. and Pyne, S. 2010. Bayesian inference for finite mixtures of univariate and multivariate skew-normal and skew-t distributions. Biostatistics, 11, 317–336. [221, 222]
123. Fung, T. and Seneta, E. 2010. Tail dependence for two skew t distributions. Statist. Probab. Lett., 80, 784–791. [193]
124. Genton, M. G. (ed.). 2004. Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [186]
125. Genton, M. G. 2005. Discussion of ‘The skew-normal’. Scand. J. Statist., 32, 189–198. [204]
126. Genton, M. G. and Loperfido, N. 2005. Generalized skew-elliptical distributions and their quadratic forms. Ann. Inst. Statist. Math., 57, 389–401. [11, 175]
127. Genton, M. G., He, L., and Liu, X. 2001. Moments of skew-normal random vectors and their quadratic forms. Statist. Probab. Lett., 51, 319–325. [142]
128. Ghizzoni, T., Roth, G., and Rudari, R. 2010. Multivariate skew-t approach to the design of accumulation risk scenarios for the flooding hazard. Advances inWater Resources, 33, 1243–1255. [186]
129. Ghizzoni, T., Roth, G., and Rudari, R. 2012. Multisite flooding hazard assessment in the Upper Mississippi River. J. Hydrology, 412–413, 101–113. [186]
130. Ghosh, P., Branco, M. D., and Chakraborty, H. 2007. Bivariate random effect model using skew-normal distribution with application to HIV–RNA. Statist. Med., 26, 1255–1267. [220]
131. Giorgi, E. 2012. Indici non Parametrici per Famiglie Parametriche con Particolare Riferimento alla t Asimmetrica. Tesi di laurea magistrale, Università di Padova. http://tesi.cab.unipd.it/40101/. [180]
132. González-Farías, G., Domínguez-Molina, J. A., and Gupta, A. K. 2004a. Additive properties of skew normal random vectors. J. Statist. Plann. Inference, 126, 521– 534. [200]
133. González-Farías, G., Domínguez-Molina, J. A., and Gupta, A. K. 2004b. The closed skew-normal distribution. Chap. 2, pages 25–42 of: Genton, M. G. (ed.), Skewelliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [200]
134. Greco, L. 2011. Minimum Hellinger distance based inference for scalar skew-normal and skew-t distributions. Test, 20, 120–137. [82]
135. Grilli, L. and Rampichini, C. 2010. Selection bias in linear mixed models. Metron, LXVIII, 309–329. [200]
136. Guolo, A. 2008. A flexible approach to measurement error correction in case-control studies. Biometrics, 64, 1207–1214. [216]
137. Gupta, A. K. 2003. Multivariate skew t-distribution. Statistics, 37, 359–363. [105, 178]
138. Gupta, A. K. and Huang, W.-J. 2002. Quadratic forms in skew normal variates. J. Math. Anal. Appl., 273, 558–564. [142]
139. Gupta, A. K. and Kollo, T. 2003. Density expansions based on the multivariate skew normal distribution. Sankhyā, 65, 821–835. [216]
140. Gupta, A. K., Chang, F. C., and Huang, W.-J. 2002. Some skew-symmetric models. Random Op. Stochast. Eq., 10, 133–140. [120]
141. Gupta, A. K., González-Farías, G., and Domínguez-Molina, J. A. 2004. A multivariate skew normal distribution. J. Multiv. Anal., 89, 181–190. [200]
142. Gupta, R. C. and Brown, N. 2001. Reliability studies of the skew-normal distribution and its application to a strength–stress model. Commun. Statist. Theory Methods, 30, 2427–2445. [225]
143. Gupta, R. C. and Gupta, R. D. 2004. Generalized skew normal model. Test, 13, 501– 524. [202]
144. Hallin, M. and Ley, C. 2012. Skew-symmetric distributions and Fisher information – a tale of two densities. Bernoulli, 18, 747–763. [188]
145. Hampel, F. R., Rousseeuw, P. J., Ronchetti, E. M., and Stahel, W. A. 1986. Robust Statistics: The Approach Based on Influence Functions. New York: J.Wiley & Sons. [116]
146. Hansen, B. 1994. Autoregressive conditional density estimation. Int. Econ. Rev., 35, 705–730. [22]
147. Harrar, S. W. and Gupta, A. K. 2008. On matrix variate skew-normal distributions. Statistics, 42, 179–184. [212]
148. Healy, M. J. R. 1968. Multivariate normal plotting. Appl. Statist., 17, 157–161. [144]
149. Heckman, J. J. 1976. The common structure of statistical models of truncation, sample selection and limited dependent variables, and a simple estimator for such models. Ann. Econ. Soc. Meas., 5, 475–492. [89, 90]
150. Henze, N. 1986. A probabilistic representation of the ‘skew-normal’ distribution. Scand. J. Statist., 13, 271–275. [43, 54]
151. Hernández-Sánchez, E. and Scarpa, B. 2012. A wrapped flexible generalized skewnormal model for a bimodal circular distribution of wind directions. Chil. J. Statist., 3, 131–143. [208]
152. Hill, M. A. and Dixon, W. J. 1982. Robustness in real life: a study of clinical laboratory data. Biometrics, 38, 377–396. [96]
153. Hinkley, D. V. and Revankar, N. S. 1977. Estimation of the Pareto law from underreported data. J. Economet., 5, 1–11. [22]
154. Ho, H.-J. and Lin, T.-I. 2010. Robust linear mixed models using the skew t distribution with application to schizophrenia data. Biometr. J., 52, 449–469. [220]
155. Huang, W.-J. and Chen, Y.-H. 2007. Generalized skew-Cauchy distribution. Statist. Probab. Lett., 77, 1137–1147. [19]
156. Huber, P. J. 1981. Robust Statistics. New York: J.Wiley & Sons. [116]
157. Huber, P. J. and Ronchetti, E. M. 2009. Robust Statistics, 2nd edn. New York: J.Wiley & Sons. [118]
158. Jamalizadeh, A. and Balakrishnan, N. 2008. On order statistics from bivariate skewnormal and skew-tν distributions. J. Statist. Plann. Inference, 138, 4187–4197. [202]
159. Jamalizadeh, A. and Balakrishnan, N. 2009. Order statistics from trivariate normal and tν-distributions in terms of generalized skew-normal and skew-tν distributions. J. Statist. Plann. Inference, 139, 3799–3819. [202, 203]
160. Jamalizadeh, A. and Balakrishnan, N. 2010. Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions. J. Multiv. Anal., 101, 1412–1427. [201, 203]
161. Jamalizadeh, A., Khosravi, M., and Balakrishnan, N. 2009a. Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t. Comp. Statist. Data An., 53, 847–852. [121]
162. Jamalizadeh, A., Mehrali, Y., and Balakrishnan, N. 2009b. Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t. Comp. Statist. Data An., 53, 4018–4027. [183, 186]
163. Jamshidi, A. A. and Kirby, M. J. 2010. Skew-radial basis function expansions for empirical modeling. SIAM J. Sci. Comput., 31, 4715–4743. [217]
164. Jara, A., Quintana, F., and San Martín, E. 2008. Linear mixed models with skewelliptical distributions: a Bayesian approach. Comp. Statist. Data An., 52, 5033– 5045. [220]
165. Javier, W. and Gupta, A. K. 2009. Mutual information for certain multivariate distributions. Far East J. Theor. Stat., 29, 39–51. [142]
166. Jiménez-Gamero, M. D., Alba-Fernández, V., Muñoz-García, J., and Chalco-Cano, Y. 2009. Goodness-of-fit tests based on empirical characteristic functions. Comp. Statist. Data An., 53, 3957–3971. [146]
167. Jones, M. C. 2001. A skew t distribution. Pages 269–278 of: Charalambides, C. A., Koutras, M. V., and Balakrishnan, N. (eds), Probability and Statistical Models with Applications: A Volume in Honor of Theophilos Cacoullos. London: Chapman & Hall. [106]
168. Jones, M. C. 2012. Relationship between distributions with certain symmetries. Statist. Probab. Lett., 82, 1737–1744. [21]
169. Jones, M. C. 2013. Generating distributions by transformation of scale. Statist. Sinica, to appear. [20, 21]
170. Jones, M. C. and Faddy, M. J. 2003. A skew extension of the t-distribution, with applications. J. R. Statist. Soc., ser. B, 65, 159–174. [106, 108]
171. Jones, M. C. and Larsen, P. V. 2004. Multivariate distributions with support above the diagonal. Biometrika, 91, 975–986. [107]
172. Kano, Y. 1994. Consistency property of elliptical probability density functions. J. Multiv. Anal., 51, 139–147. [107, 171]
173. Kim, H. J. 2002. Binary regression with a class of skewed t link models. Commun. Statist. Theory Methods, 31, 1863–1886. [227]
174. Kim, H.-J. 2008. A class of weighted multivariate normal distributions and its properties. J. Multiv. Anal., 99, 1758–1771. [166]
175. Kim, H.-M. and Genton, M. G. 2011. Characteristic functions of scale mixtures of multivariate skew-normal distributions. J. Multiv. Anal., 102, 1105–1117. [51, 175]
176. Kim, H.-M. and Mallick, B. K. 2003. Moments of random vectors with skew t distribution and their quadratic forms. Statist. Probab. Lett., 63, 417–423. Corrigendum: vol. 79 (2009), 2098–2099. [178]
177. Kim, H.-M. and Mallick, B. K. 2004. A Bayesian prediction using the skew Gaussian distribution. J. Statist. Plann. Inference, 120, 85–101. [224]
178. Kim, H.-M., Ha, E. and Mallick, B. K. 2004. Spatial prediction of rainfall using skewnormal processes. Chap. 16, pages 279–289 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [224]
179. Kozubowski, T. J. and Nolan, J. P. 2008. Infinite divisibility of skew Gaussian and Laplace laws. Statist. Probab. Lett., 78, 654–660. [54]
180. Lachos, V. H., Ghosh, P., and Arellano-Valle, R. B. 2010a. Likelihood based inference for skew-normal independent linear mixed models. Statist. Sinica, 20, 303–322. [175]
181. Lachos, V. H., Labra, F. V., Bolfarine, H., and Ghosh, P. 2010b. Multivariate measurement error models based on scale mixtures of the skew-normal distribution. Statistics, 44, 541–556. Available online 28 October 2009. [179]
182. Lagos Á lvarez, B. and Jiménez Gamero, M. D. 2012. A note on bias reduction of maximum likelihood estimates for the scalar skew t distribution. J. Statist. Plann. Inference, 142, 608–612. Available online 8 September 2011. [112]
183. Lange, K. L., Little, R. J. A., and Taylor, J. M. G. 1989. Robust statistical modeling using the t-distribution. J. Amer. Statist. Assoc., 84, 881–896. [95]
184. Lauritzen, S. L. 1996. Graphical Models. Oxford: Oxford University Press. [154]
185. Leadbetter, M. R., Lindgren, G., and Rootzén, H. 1983. Extremes and Related Properties of Random Sequences and Processes. Berlin: Springer-Verlag. [55, 122]
186. Lee, S. and McLachlan, G. J. 2012. Finite mixtures of multivariate skew t-distributions: some recent and new results. Statist. Comput., to appear. Available online 20 October 2012. [192]
187. Lee, S., Genton, M. G., and Arellano-Valle, R. B. 2010. Perturbation of numerical confidential data via skew-t distributions. Manag. Sci., 56, 318–333. [185]
188. Ley, C. and Paindaveine, D. 2010a. On Fisher information matrices and profile loglikelihood functions in generalized skew-elliptical models. Metron, LXVIII, 235– 250. [180]
189. Ley, C. and Paindaveine, D. 2010b. On the singularity of multivariate skew-symmetric models. J. Multiv. Anal., 101, 1434–1444. [188]
190. Lin, G. D. and Stoyanov, J. 2009. The logarithmic skew-normal distributions are moment-indeterminate. J. Appl. Prob., 46, 909–916. [54]
191. Lin, T. I., 2009. Maximum likelihood estimation for multivariate skew normal mixture models. J. Multiv. Anal., 100, 257–265. [221]
192. Lin, T.-I. 2010. Robust mixture modeling using multivariate skew t distributions. Statist. Comput., 20, 343–356. [192, 221]
193. Lin, T.-I. and Lin, T.-C. 2011. Robust statistical modelling using the multivariate skew t distribution with complete and incomplete data. Statist. Model., 11, 253–277. [192]
194. Lin, T. I., Lee, J. C., and Hsieh, W. J. 2007a. Robust mixture modeling using the skew t distribution. Statist. and Comput., 17, 81–92. [221]
195. Lin, T. I., Lee, J. C., and Yen, S. Y. 2007b. Finite mixture modelling using the skew normal distribution. Statist. Sinica, 17, 909–927. [94, 221]
196. Liseo, B. 1990. La classe delle densità normali sghembe: aspetti inferenziali da un punto di vista bayesiano. Statistica, L, 59–70. [77]
197. Liseo, B. and Loperfido, N. 2003. A Bayesian interpretation of the multivariate skewnormal distribution. Statist. Probab. Lett., 61, 395–401. [200]
198. Liseo, B. and Loperfido, N. 2006. A note on reference priors for the scalar skew-normal distribution. J. Statist. Plann. Inference, 136, 373–389. [82, 83]
199. Loperfido, N. 2001. Quadratic forms of skew-normal random vectors. Statist. Probab. Lett., 54, 381–387. [141]
200. Loperfido, N. 2002. Statistical implications of selectively reported inferential results. Statist. Probab. Lett., 56, 13–22. [43]
201. Loperfido, N. 2008. Modelling maxima of longitudinal contralateral observations. Test, 17, 370–380. [141]
202. Loperfido, N. 2010. Canonical transformations of skew-normal variates. Test, 19, 146– 165. [141]
203. Lysenko, N., Roy, P., and Waeber, R. 2009. Multivariate extremes of generalized skewnormal distributions. Statist. Probab. Lett., 79, 525–533. [23, 193]
204. Ma, Y. and Genton, M. G. 2004. Flexible class of skew-symmetric distributions. Scand. J. Statist., 31, 459–468. [50, 203, 204]
205. Ma, Y., Genton, M. G., and Tsiatis, A. A. 2005. Locally efficient semiparametric estimators for generalized skew-elliptical distributions. J. Amer. Statist. Assoc., 100, 980–989. [205]
206. Maddala, G. S. 2006. Limited dependent variables models. In: Encyclopedia of Statistical Sciences. New York: J.Wiley & Sons. [89, 90]
207. Malkovich, J. F. and Afifi, A. A. 1973. Measures of multivariate skewness and kurtosis with applications. J. Amer. Statist. Assoc., 68, 176–179. [138]
208. Marchenko, Y. V. and Genton, M. G. 2012. A Heckman selection-t model. J. Amer. Statist. Assoc., 107, 304–317. [185, 186]
209. Mardia, K. 1970. Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519–530. [132]
210. Mardia, K. V. 1974. Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies. Sankhyā, ser. B, 36, 115–128. [132, 174]
211. Mardia, K. V. and Jupp, P. E. 1999. Directional Statistics. New York: J.Wiley & Sons. [208]
212. Mardia, K. V., Kent, J. T., and Bibby, J. M. 1979. Multivariate Analysis. NewYork: Academic Press. [137]
213. Martínez, E. H., Varela, H., Gómez, H. W., and Bolfarine, H. 2008. A note on the likelihood and moments of the skew-normal distribution. SORT, 32, 57–66. [54, 94]
214. Mateu-Figueras, G. and Pawlowsky-Glahn, V. 2007. The skew-normal distribution on the simplex. Commun. Statist. Theory Methods, 36, 1787–1802. [211]
215. Mateu-Figueras, G., Pawlowsky-Glahn, V., and Barceló-Vidal, C. 2005. Additive logistic skew-normal on the simplex. Stochast. Environ. Res. Risk Assess., 19, 205– 214. [211]
216. Mateu-Figueras, G., Puig, P., and Pewsey, A. 2007. Goodness-of-fit tests for the skewnormal distribution when the parameters are estimated from the data. Commun. Statist. Theory Methods, 36, 1735–1755. [87]
217. Mazzuco, S. and Scarpa, B. 2013. Fitting age-specific fertility rates by a flexible generalized skew-normal probability density function. J. R. Statist. Soc., ser. A, under revision. [217]
218. McLachlan, G. J. and Peel, D. 2000. Finite Mixture Models. New York: J.Wiley & Sons. [221]
219. Meeusen, W. and van den Broeck, J. 1977. Efficiency estimation from Cobb–Douglas production function with composed error. Int. Econ. Rev., 18, 435–444. [91]
220. Meintanis, S. G. 2007. A Kolmogorov–Smirnov type test for skew normal distributions based on the empirical moment generating function. J. Statist. Plann. Inference, 137, 2681–2688. 5th St. Petersburg Workshop on Simulation. [87]
221. Meintanis, S. G. and Hlávka, Z. 2010. Goodness-of-fit tests for bivariate and multivariate skew-normal distributions. Scand. J. Statist., 37, 701–714. [146]
222. Meucci, A. 2006. Beyond Black–Litterman: views on non-normal markets. Risk Magazine, 19, 87–92. [186]
223. Minozzo, M. and Ferracuti, L. 2012. On the existence of some skew-normal stationary processes. Chil. J. Statist., 3, 159–172. [224]
224. Montenegro, L. C., Lachos, V. H., and Bolfarine, H. 2009. Local influence analysis for skew-normal linear mixed models. Commun. Statist. Theory Methods, 38, 484–496. [220]
225. Mudholkar, G. S. and Hutson, A. D. 2000. The epsilon-skew-normal distribution for analysing near-normal data. J. Statist. Plann. Inference, 83, 291–309. [22]
226. Nagaraja, H. N. 1982. A note on linear functions of ordered correlated normal random variables. Biometrika, 69, 284–285. [52]
227. Nathoo, F. S. 2010. Space–time regression modeling of tree growth using the skew-t distribution. Environmetrics, 21, 817–833. [220]
228. Naveau, P., Genton, M. G., and Ammann, C. 2004. Time series analysis with a skewed Kalman filter. Chap. 15, pages 259–278 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [224]
229. Naveau, P., Genton, M. G., and Shen, X. 2005. A skewed Kalman filter. J. Multiv. Anal., 94, 382–400. [224]
230. Nelson, L. S. 1964. The sum of values from a normal and a truncated normal distribution. Technometrics, 6, 469–471. [42]
231. O’Hagan, A. and Leonard, T. 1976. Bayes estimation subject to uncertainty about parameter constraints. Biometrika, 63, 201–202. [42]
232. Owen, D. B. 1956. Tables for computing bivariate normal probabilities. Ann. Math. Statist., 27, 1075–1090. [34, 234, 235]
233. Owen, D. B. 1957. The bivariate normal probability distribution. Tech. rept. SC-3831 (TR), Systems Analysis. Sandia Corporation. Available from the Office of Technical Services, Dept. of Commerce, Washington 25, D.C. [235]
234. Pacillo, S. 2012. Selection of conditional independence graph models when the distribution is extended skew normal. Chil. J. Statist., 3, 183–194. [158]
235. Padoan, S. A. 2011. Multivariate extreme models based on underlying skew-t and skew-normal distributions. J. Multiv. Anal., 102, 977–991. [53, 122, 193]
236. Pérez Rodríguez, P., and Villaseñor Alva, J. A. 2010. On testing the skew normal hypothesis. J. Statist. Plann. Inference, 140, 3148–3159. [87]
237. Pewsey, A. 2000a. Problems of inference for Azzalini’s skew-normal distribution. J. Appl. Statist., 27, 859–870. [76]
238. Pewsey, A. 2000b. The wrapped skew-normal distribution on the circle. Commun. Statist. Theory Methods, 29, 2459–2472. [51, 208]
239. Pewsey, A. 2003. The characteristic functions of the skew-normal and wrapped skewnormal distributions. Pages 4383–4386 of: XXVII Congreso Nacional de Estadistica e Investigación Operativa. SEIO, Lleida (España). [51, 208]
240. Pewsey, A. 2006a. Modelling asymmetrically distributed circular data using the wrapped skew-normal distribution. Environ. Ecol. Statist., 13, 257–269. [208]
241. Pewsey, A. 2006b. Some observations on a simple means of generating skew distributions. Pages 75–84 of: Balakrishnan, N., Castillo, E., and Sarabia, J. M. (eds), Advances in Distribution Theory, Order Statistics and Inference. Boston, MA: Birkhäuser. [94, 188]
242. Potgieter, C. J. and Genton, M. G. 2013. Characteristic function-based semiparametric inference for skew-symmetric models. Scand. J. Statist., 40, 471–490. Available online 26 December 2012. [207]
243. Pourahmadi, M. 2007. Skew-normal ARMA models with nonlinear heteroscedastic predictors. Commun. Statist. Theory Methods, 36, 1803–1819. [222]
244. Pyne, S., Hu, X., Wang, K., Rossin, E., Lin, T.-I., Maier, L. M., et al. 2009. Automated high-dimensional flow cytometric data analysis. PNAS, 106, 8519–8524. [221]
245. R Development Core Team. 2011. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3- 900051-07-0. [75]
246. Rao, C. R. 1973. Linear Statistical Inference and its Applications, 2nd edn. New York: J.Wiley & Sons. [137]
247. Roberts, C. 1966. A correlation model useful in the study of twins. J. Amer. Statist. Assoc., 61, 1184–1190. [42, 54]
248. Rotnitzky, A., Cox, D. R., Bottai, M., and Robins, J. 2000. Likelihood-based inference with singular information matrix. Bernoulli, 6, 243–284. [68, 69, 72]
249. Sahu, S. K. and Dey, D. K. 2004. On a Bayesian multivariate survival model with a skewed frailty. Chap. 19, pages 321–338 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [192, 228]
250. Sahu, K., Dey, D. K., and Branco, M. D. 2003. A new class of multivariate skew distributions with applications to Bayesian regression models. Canad. J. Statist., 31, 129–150. Corrigendum: vol. 37 (2009), 301–302. [190, 192, 194, 200]
251. Salvan, A. 1986. Test localmente più potenti tra gli invarianti per la verifica dell’ipotesi di normalità. Pages 173–179 of: Atti della XXXIII Riunione Scientifica della Società Italiana di Statistica, vol. II. Bari: Cacucci. [86]
252. Sartori, N. 2006. Bias prevention of maximum likelihood estimates for scalar skew normal and skew t distributions. J. Statist. Plann. Inference, 136, 4259–4275. [79]
253. Serfling, R. 2006. Multivariate symmetry and asymmetry. Pages 5338–5345 of: Kotz, S., Balakrishnan, N., Read, C. B., and Vidakovic, B. (eds), Encyclopedia of Statistical Sciences, II edn, vol. 8. New York: J.Wiley & Sons. [2]
254. Sharafi, M. and Behboodian, J. 2008. The Balakrishnan skew-normal density. Statist. Papers, 49, 769–778. [202]
255. Shun, Z., Lan, K. K. G., and Soo, Y. 2008. Interim treatment selection using the normal approximation approach in clinical trials. Statist. Med., 27, 597–618. [225]
256. Šidák, Z. 1967. Rectangular confidence regions for the means of multivariate normal distributions. J. Amer. Statist. Assoc., 62, 626–633. [166]
257. Soriani, N. 2007. La Distribuzione t Asimmetrica: Analisi Discriminante e Regioni di Tollerenza. Tesi di laurea, Facoltà di Scienze Statistiche, Università di Padova. http://tesi.cab.unipd.it/7115/. [179]
258. Stanghellini, E. and Wermuth, N. 2005. On the identification of path analysis models with one hidden variable. Biometrika, 92, 337–350. [158]
259. Stingo, F. C., Stanghellini, E., and Capobianco, R. 2011. On the estimation of a binary response model in a selected population. J. Statist. Plann. Inference, 141, 3293– 3303. [227]
260. Subbotin, M. T. 1923. On the law of frequency of error. Mat. Sbornik, 31, 296–301. [96]
261. Tchumtchoua, S. and Dey, D. K. 2007. Bayesian estimation of stochastic frontier models with multivariate skew t error terms. Commun. Statist. Theory Methods, 36, 907–916. [192, 225]
262. Thompson, K. R. and Shen, Y. 2004. Coastal flooding and the multivariate skew-t distribution. Chap. 14, pages 243–258 of: Genton, M. G. (ed.), Skew-elliptical Distributions and their Applications: A Journey Beyond Normality. Boca Raton, FL: Chapman & Hall/CRC. [186]
263. Tong, H. 1990. Non-linear Time Series: A Dynamical System Approach. Oxford: Oxford University Press. [223]
264. Tsai, T.-R. 2007. Skew normal distribution and the design of control charts for averages. Int. J. Rel. Qual. Saf. Eng., 14, 49–63. [225]
265. Tyler, D. E., Critchley, F., Dümbgen, L., and Oja, H. 2009. Invariant co-ordinate selection (with discussion). J. R. Statist. Soc., ser. B, 71, 549–692. [160]
266. Umbach, D. 2006. Some moment relationships for skew-symmetric distributions. Statist. Probab. Lett., 76, 507–512. [11]
267. Umbach, D. 2007. The effect of the skewing distribution on skew-symmetric families. Soochow Journal of Mathematics, 33, 657–668. [47]
268. Umbach, D. and Jammalamadaka, S. R. 2009. Building asymmetry into circular distributions. Statist. Probab. Lett., 79, 659–663. [208, 210]
269. Umbach, D. and Jammalamadaka, S. R. 2010. Some moment properties of skewsymmetric circular distributions. Metron, LXVIII, 265–273. [208]
270. Van Oost, K., Van Muysen, W., Govers, G., Heckrath, G., Quine, T. A., and Poesen, J. 2003. Simulation of the redistribution of soil by tillage on complex topographies. European J. Soil Sci., 54, 63–76. [160]
271. Vernic, R. 2006. Multivariate skew-normal distributions with applications in insurance. Insurance: Math. Econ., 38, 413–426. [159, 160]
272. Vianelli, S. 1963. La misura della variabilità condizionata in uno schema generale delle curve normali di frequenza. Statistica, 33, 447–474. [96]
273. Walls, W. D. 2005. Modeling heavy tails and skewness in film returns. Appl. Financial Econ., 15, 1181–1188. [119]
274. Wang, J. and Genton, M. G. 2006. The multivariate skew-slash distribution. J. Statist. Plann. Inference, 136, 209–220. [195]
275. Wang, J., Boyer, J., and Genton, M. G. 2004. A skew-symmetric representation of multivariate distributions. Statist. Sinica, 14, 1259–1270. [11, 175]
276. Weinstein, M. A. 1964. The sum of values from a normal and a truncated normal distribution. Technometrics, 6, 104–105. [42]
277. Whitt, W. 2006. Stochastic ordering. Pages 8260–8264 of: Kotz, S., Balakrishnan, N., Read, C. B., and Vidakovic, B. (eds), Encyclopedia of Statistical Sciences, II edn, vol. 13. New York: J.Wiley & Sons. [10]
278. Yohai, V. J. 1987. High breakdown-point and high efficiency robust estimates for regression. Ann. Statist., 15, 642–656. [112, 114, 115]
279. Zacks, S. 1981. Parametric Statistical Inference. Oxford: Pergamon Press. [26]
280. Zhang, H. and El-Shaarawi, A. 2010. On spatial skew-Gaussian processes and applications. Environmetrics, 21, 33–47. Available online 17 March 2009. [223]
281. Zhou, T. and He, X. 2008. Three-step estimation in linear mixed models with skew-t distributions. J. Statist. Plann. Inference, 138, 1542–1555. [220]