×

An overview on the progeny of the skew-normal family – a personal perspective. (English) Zbl 07451360

Summary: In the last two decades or so, much work has been dedicated to the portion of distribution theory stemming from the skew-normal distribution and its ramification. This contribution presents an outline of the theme, without attempting a detailed review, which would be unfeasible, given the amount of available material. The aim is to present a panoramic view of the theme, leaving out the fine details, with rather more emphasis on the evolution of the underlying ideas and on the breath of the overall developments, as for range of specific directions considered.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E10 Characterization and structure theory of statistical distributions
60Exx Distribution theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abe, T.; Fujisawa, H.; Kawashima, T.; Ley, C., EM algorithm using overparameterization for the multivariate skew-normal distribution, Econometr. Stat., 19, 151-168 (2021)
[2] Abe, T.; Pewsey, A., Sine-skewed circular distributions, Stat. Pap., 52, 683-707 (2011) · Zbl 1434.62023
[3] Adcock, C. J., Exploiting skewness to build an optimal hedge fund with a currency overlay, Eur. J. Finance, 11, 445-462 (2005)
[4] Adcock, C. J., Extensions of Stein’s lemma for the skew-normal distribution, Commun. Stat. Theory Methods, 36, 1661-1671 (2007) · Zbl 1315.62016
[5] Adcock, C. J., Asset pricing and portfolio selection based on the multivariate extended skew-Student-\(t\) distribution, Ann. Oper. Res., 176, 221-234 (2010) · Zbl 1233.91112
[6] Adcock, C. J., Mean-variance-skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution, European J. Oper. Res., 234, 392-401 (2014), Available online 20 July 2013 · Zbl 1304.91174
[7] Adcock, C.; Azzalini, A., A selective overview of skew-elliptical and related distributions and of their applications, Symmetry, 12, 118 (2020)
[8] Adcock, C. J.; Shutes, K., Portfolio selection based on the multivariate skew normal distribution, (Skulimowski, A. M.J., Financial Modelling: Proceedings of the 23th Meeting of the EURO Working Group for Commodities and Financial Modelling (1999), Progress and Business Publishers: Progress and Business Publishers Kraków), 167-177, Available in 2001
[9] Aigner, D. J.; Lovell, C. A.K.; Schmidt, P., Formulation and estimation of stochastic frontier production function model, J. Econometrics, 6, 21-37 (1977) · Zbl 0366.90026
[10] Ameijeiras-Alonso, J.; Ley, C., Sine-skewed toroidal distributions and their application in protein bioinformatics, Biostatistics (2020), in press, Available online 02 October 2020
[11] Amiri, M.; Balakrishnan, N., Hessian and increasing-hessian orderings of scale-shape mixtures of multivariate skew-normal distributions and applications, J. Comput. Appl. Math., 402, Article 113801 pp. (2022) · Zbl 1475.60041
[12] Arellano-Valle, R. B., The information matrix of the multivariate skew-\(t\) distribution, Metron, LXVIII, 371-386 (2010) · Zbl 1301.62051
[13] Arellano-Valle, R. B.; Azzalini, A., On the unification of families of skew-normal distributions, Scand. J. Stat., 33, 561-574 (2006), (Corrigendum) · Zbl 1117.62051
[14] Arellano-Valle, R. B.; Azzalini, A., The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal., 99, 1362-1382 (2008), Corrigendum: 100 (2009) p. 816 · Zbl 1140.62040
[15] Arellano-Valle, R. B.; Azzalini, A., Some properties of the unified skew-normal distribution, Statist. Papers (2021), in press
[16] Arellano-Valle, R. B.; Bolfarine, H.; Lachos, V. H., Skew-normal linear mixed models, J. Data Sci., 3, 415-438 (2005)
[17] Arellano-Valle, R. B.; Bolfarine, H.; Lachos, V. H., BayesIan inference for skew-normal linear mixed models, J. Appl. Stat., 34, 663-682 (2007) · Zbl 07252103
[18] Arellano-Valle, R. B.; Branco, M. D.; Genton, M. G., A unified view on skewed distributions arising from selections, Canad. J. Stat., 34, 581-601 (2006) · Zbl 1121.60009
[19] Arellano-Valle, R. B.; del Pino, G.; San Martín, E., Definition and probabilistic properties of skew-distributions, Statist. Probab. Lett., 58, 111-121 (2002) · Zbl 1045.62046
[20] Arellano-Valle, R. B.; Ferreira, C. S.; Genton, M. G., Scale and shape mixtures of multivariate skew-normal distributions, J. Multivariate Anal., 166, 98-110 (2018) · Zbl 06869753
[21] Arellano-Valle, R. B.; Genton, M. G., On fundamental skew distributions, J. Multivariate Anal., 96, 93-116 (2005) · Zbl 1073.62049
[22] Arellano-Valle, R. B.; Genton, M. G., Multivariate extended skew-\(t\) distributions and related families, Metron, LXVIII, 201-234 (2010) · Zbl 1301.62016
[23] Arellano-Valle, R. B.; Genton, M. G., Multivariate unified skew-elliptical distributions, Chil. J. Stat., 1, 17-33 (2010) · Zbl 1213.62087
[24] Arellano-Valle, R. B.; Gómez, H. W.; Quintana, F. A., A new class of skew-normal distributions, Commun. Stat. Theory Methods, 33, 1465-1480 (2004) · Zbl 1134.60304
[25] Arellano-Valle, R. B.; Ozán, S.; Bolfarine, H.; Lachos, V. H., Skew-normal measurement error models, J. Multivariate Anal., 96, 265-281 (2005) · Zbl 1077.62043
[26] Arnold, B. C.; Beaver, R. J., Hidden truncation models, Sankhyā, 62, 22-35 (2000) · Zbl 0973.62041
[27] Azzalini, A., A class of distributions which includes the normal ones, Scand. J. Stat., 12, 171-178 (1985) · Zbl 0581.62014
[28] Azzalini, A., Further results on a class of distributions which includes the normal ones, Statistica, XLVI, 199-208 (1986), Reprinted with annotations and corrigenda in 80 (2020) 161-175 · Zbl 0606.62013
[29] Azzalini, A., A note on regions of given probability of the skew-normal distribution, Metron, LIX, 27-34 (2001) · Zbl 1004.62501
[30] Azzalini, A., Selection models under generalized symmetry settings, Ann. Inst. Statist. Math., 64, 737-750 (2012), Available online 05 March 2011 · Zbl 1253.62037
[31] Azzalini, A., The Skew-Normal and Related Families, IMS Monographs (2014), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 1338.62007
[32] Azzalini, A., Flexible distributions as an approach to robustness: the skew-\(t\) case, (Agostinelli, C.; Basu, A.; Filzmoser, P.; Mukherjee, D., Recent Advances in Robust Statistics: Theory and Applications (2016), Springer India), 1-16 · Zbl 1359.62090
[33] Azzalini, A., The R package : The skew-normal and related distributions such as the skew-\(t\) and the SUN (version 2.0.0), ((2021), Università degli Studi di Padova: Università degli Studi di Padova Italia)
[34] Azzalini, A.; Arellano-Valle, R. B., Maximum penalized likelihood estimation for skew-normal and skew-\(t\) distributions, J. Statist. Plann. Inference, 143, 419-433 (2013), Available online 30 June 2012 · Zbl 1254.62020
[35] Azzalini, A.; Capitanio, A., Statistical applications of the multivariate skew normal distribution, J. R. Stat. Soc. Ser. B Stat. Methodol., 61, 579-602 (1999), Full paper at arXiv.org:0911.2093 · Zbl 0924.62050
[36] Azzalini, A.; Capitanio, A., Distributions generated by perturbation of symmetry with emphasis on a multivariate skew \(t\) distribution, J. R. Statist. Soc. B, 65, 367-389 (2003), Full paper at arXiv.org:0911.2342 · Zbl 1065.62094
[37] Azzalini, A.; Dalla Valle, A., The multivariate skew-normal distribution, Biometrika, 83, 715-726 (1996) · Zbl 0885.62062
[38] Azzalini, A.; Genton, M. G., Robust likelihood methods based on the skew-\(t\) and related distributions, Int. Statist. Rev., 76, 106-129 (2008) · Zbl 1206.62102
[39] Azzalini, A.; Genton, M. G.; Scarpa, B., Invariance-based estimating equations for skew-symmetric distributions, Metron, LXVIII, 275-298 (2010) · Zbl 1301.62032
[40] Azzalini, A.; Regoli, G., Some properties of skew-symmetric distributions, Ann. Inst. Statist. Math., 64, 857-879 (2012), Available online 09 September 2011 · Zbl 1253.62038
[41] Azzalini, A.; Regoli, G., The work of Fernando de Helguero on non-normality arising from selection, Chil. J. Stat., 3, 113-129 (2012) · Zbl 1449.62001
[42] Azzalini, A.; Regoli, G., Modulation of symmetry for discrete variables and some extensions, Stat, 3, 56-67 (2014)
[43] Azzalini, A.; Regoli, G., On symmetry-modulated distributions: revisiting an old result and a step further, Stat, 7, Article e171 pp. (2018)
[44] Bagnato, L.; Minozzo, M., A latent variable approach to modelling multivariate geostatistical skew-normal data, (Robust Mixture Modeling Based on Scale Mixtures of Skew-Normal Distributions, Vol. 54 (2010), Comput. Stat. Data An.), 2926-2941
[45] Basso, R. M.; Lachos, V. H.; Cabral, C. R.B.; Ghosh, P., Robust mixture modeling based on scale mixtures of skew-normal distributions, Comput. Stat. Data An., 54, 2926-2941 (2010) · Zbl 1284.62193
[46] Bazán, J. L.; Branco, M. D.; Bolfarine, H., A skew item response model, Bayesian Anal., 1, 861-892 (2006) · Zbl 1331.62448
[47] Beranger, B.; Padoan, S. A.; Sisson, S. A., Models for extremal dependence derived from skew-symmetric families, Scand. J. Stat., 44, 21-45 (2017), Available online 13 September 2016 · Zbl 1361.62009
[48] Beranger, B.; Padoan, S. A.; Xu, Y.; Sisson, S. A., Extremal properties of the univariate extended skew-normal distribution, part A, Statist. Probab. Lett., 147, 73-82 (2019), Available online 5 December 2018 · Zbl 1412.62051
[49] Beranger, B.; Padoan, S. A.; Xu, Y.; Sisson, S. A., Extremal properties of the multivariate extended skew-normal distribution, part B, Statist. Probab. Lett., 147, 105-114 (2019), Available online 7 December 2018 · Zbl 1412.62052
[50] Birnbaum, Z. W., Effect of linear truncation on a multinormal population, Ann. Math. Stat., 21, 272-279 (1950) · Zbl 0038.09201
[51] Bolfarine, H.; Lachos, V. H., Skew probit measurement error models, Stat. Methodol., 4, 1-12 (2007) · Zbl 1248.62176
[52] Bolfarine, H.; Montenegro, L. C.; Lachos, V. H., Influence diagnostics for skew-normal linear mixed models, Sankhyā, 69, 648-670 (2007) · Zbl 1193.62123
[53] Branco, M. D.; Dey, D. K., A general class of multivariate skew-elliptical distributions, J. Multivariate Anal., 79, 99-113 (2001) · Zbl 0992.62047
[54] Branco, M. D.; Genton, M. G.; Liseo, B., Objective Bayesian analysis of skew-\(t\) distributions, Scand. J. Stat., 40, 63-85 (2013) · Zbl 1259.62008
[55] Cabral, C. R.B.; Lachos, V. H.; Prates, M. O., Multivariate mixture modeling using skew-normal independent distributions, Comput. Statist. Data Anal., 56, 126-142 (2012) · Zbl 1239.62058
[56] Callegaro, A.; Iacobelli, S., The Cox shared frailty model with log-skew-normal frailties, Stat. Model., 12, 399-418 (2012) · Zbl 07257885
[57] Capitanio, A., On the canonical form of scale mixtures of skew-normal distributions, Reprinted in Statistica, 80, 145-160 (2020), arXiv.org:1207.0797. 2012
[58] Capitanio, A.; Azzalini, A.; Stanghellini, E., Graphical models for skew-normal variates, Scand. J. Stat., 30, 129-144 (2003) · Zbl 1035.60008
[59] Chang, S.-C.; Zimmerman, D. L., Skew-normal antedependence models for skewed longitudinal data, Biometrika, 103, 363-376 (2016) · Zbl 07072117
[60] Chen, M.-H.; Dey, D. K.; Shao, Q.-M., A new skewed link model for dichotomous quantal response data, J. Amer. Statist. Assoc., 94, 1172-1186 (1999) · Zbl 1072.62655
[61] Chen, J. T.; Gupta, A. K., Matrix variate skew normal distributions, Statistics, 39, 247-253 (2005) · Zbl 1070.62039
[62] Chen, L.; Pourahmadi, M.; Maadooliat, M., Regularized multivariate regression models with skew-\(t\) error distributions, J. Statist. Plann. Inference, 149, 125-139 (2014) · Zbl 1285.62073
[63] Chiogna, M., A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution, Stat. Meth. Appl., 14, 331-341 (2005) · Zbl 1103.62024
[64] Colombi, R.; Kumbhakar, S. C.; Martini, G.; Vittadini, G., Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency, J. Prod. Anal., 42, 123-136 (2014)
[65] de Helguero, F., Sulla rappresentazione analitica delle curve abnormali, (Castelnuovo, G., Atti Del IV Congresso Internazionale Dei Matematici (Roma, 6-11(Aprile 1908), Volume III, Sezione III-B (1909), R. Accademia dei Lincei: R. Accademia dei Lincei Roma), 288-299, Available at https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1908.3/ICM1908.3.ocr.pdf
[66] de Helguero, F., Sulla rappresentazione analitica delle curve statistiche, Giornale Degli Economisti XXXVIII, Serie, 2, 241-265 (1909) · JFM 40.0294.03
[67] Diallo, M. S.; Rao, J. N.K., Small area estimation of complex parameters under unit-level models with skew-normal errors, Scand. J. Stat., 45, 1092-1116 (2018) · Zbl 1410.62122
[68] Domínguez-Molina, J. A.; González-Farías, G.; Ramos-Quiroga, R., Skew-normality in stochastic frontier analysis, (Genton, Marc G., Skew-elliptical Distributions and Their Applications: a Journey Beyond Normality (2004)), 223-242
[69] Domínguez-Molina, J. A.; González-Farías, G.; Ramos-Quiroga, R.; Gupta, A. K., A matrix variate closed skew-normal distribution with applications to stochastic frontier analysis, Commun. Statist. Theory Methods, 36, 1671-1703 (2007) · Zbl 1122.62043
[70] Durante, D., Conjugate Bayes for probit regression via unified skew-normal distributions, Biometrika, 106, 765-779 (2019) · Zbl 1435.62107
[71] Fang, K.-T.; Kotz, S.; Ng, K. W., Symmetric Multivariate and Related Distributions (1990), Chapman & Hall: Chapman & Hall London
[72] Fasano, A.; Rebaudo, G.; Durante, D.; Petrone, S., A closed-form filter for binary time series, Stat. Comput., 31, Article 47 pp. (2021) · Zbl 1475.62030
[73] Ferrante, M. R.; Pacei, S., Small domain estimation of business statistics by using multivariate skew normal models, J. R. Stat. Soc. Ser. A, 180, 1057-1088 (2017)
[74] Ferraz, V. R.S.; Moura, F. A.S., Small area estimation using skew normal models, Comput. Statist. Data Anal., 56, 2864-2874 (2012) · Zbl 1255.62061
[75] Firth, D., Bias reduction of maximum likelihood estimates, Biometrika, 80, 27-38 (1993), Amendment: 82, 667 · Zbl 0769.62021
[76] Frühwirth-Schnatter, S.; Pyne, S., BayesIan inference for finite mixtures of univariate and multivariate skew-normal and skew-\(t\) distributions, Biostatistics, 11, 317-336 (2010) · Zbl 1437.62465
[77] Fung, T.; Seneta, E., Tail dependence for two skew \(t\) distributions, Statist. Probab. Lett., 80, 784-791 (2010) · Zbl 1186.62069
[78] (Genton, M. G., Skew-Elliptical Distributions and their Applications: A Journey beyond Normality (2004), Chapman & Hall/CRC: Chapman & Hall/CRC Boca Raton, FL, USA) · Zbl 1069.62045
[79] Genton, M. G.; He, L.; Liu, X., Moments of skew-normal random vectors and their quadratic forms, Statist. Probab. Lett., 51, 319-325 (2001) · Zbl 0972.62031
[80] Ghosh, P.; Bayes, C. L.; Lachos, V. H., A robust Bayesian approach to null intercept measurement error model with application to dental data, Comput. Statist. Data Anal., 53, 1066-1079 (2009) · Zbl 1452.62809
[81] Ghosh, P.; Branco, M. D.; Chakraborty, H., Bivariate random effect model using skew-normal distribution with application to HIV-RNA, Stat. Med., 26, 1255-1267 (2007)
[82] González-Farías, G.; Domínguez-Molina, J. A.; Gupta, A. K., Additive properties of skew normal random vectors, J. Statist. Plann. Inference, 126, 521-534 (2004) · Zbl 1076.62052
[83] Gupta, A. K., Multivariate skew \(t\)-distribution, Statistics, 37, 359-363 (2003) · Zbl 1037.62045
[84] Gupta, A. K.; Huang, W.-J., Quadratic forms in skew normal variates, J. Math. Anal. Appl., 273, 558-564 (2002) · Zbl 1005.62058
[85] Gupta, A. K.; Kollo, T., Density expansions based on the multivariate skew normal distribution, Sankhyā, 65, 821-835 (2003) · Zbl 1193.62091
[86] Hallin, M.; Ley, C., Skew-symmetric distributions and Fisher information – a tale of two densities, Bernoulli, 18, 747-763 (2012) · Zbl 1243.62068
[87] Hazra, A.; Reich, B. J.; Staicu, A., A multivariate spatial skewa-t process for joint modeling of extreme precipitation indexes, Environmetrics, 31, Article e2602 pp. (2020), Available online 29 October 2019
[88] Heckman, J. J., 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 (1976)
[89] Heckman, J. J., Sample selection bias as a specification error, Econometrica, 47, 153-161 (1979) · Zbl 0392.62093
[90] Henze, N., A probabilistic representation of the ‘skew-normal’ distribution, Scand. J. Stat., 13, 271-275 (1986) · Zbl 0648.62016
[91] Hernández-Sánchez, E.; Scarpa, B., A wrapped flexible generalized skew-normal model for a bimodal circular distribution of wind directions, Chil. J. Stat., 3, 131-143 (2012) · Zbl 1449.62258
[92] Huang, Y.; Dagne, G. A., Simultaneous Bayesian inference for skew-normal semiparametric nonlinear mixed-effects models with covariate measurement errors, Bayesian Anal., 7, 189-210 (2012) · Zbl 1330.62137
[93] Jamali, D.; Amiri, M.; Jamalizadeh, A., Comparison of the multivariate skew-normal random vectors based on the integral stochastic ordering, Commun. Stat. Theory Methods (2021), in press, Available online 23 March 2020
[94] Jamalizadeh, A.; Balakrishnan, N., Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions, J. Multivariate Anal., 101, 1412-1427 (2010) · Zbl 1186.62070
[95] Jamalizadeh, A.; Balakrishnan, N.; Salehi, M., Order statistics and linear combination of order statistics arising from a bivariate selection normal distribution, Statist. Probab. Lett., 80, 445-451 (2010) · Zbl 1181.62068
[96] Joe, H.; Li, H., Tail densities of skew-elliptical distributions, J. Multivariate Anal., 171, 421-435 (2019) · Zbl 1412.60075
[97] Jupp, P. E.; Regoli, G.; Azzalini, A., A general setting for symmetric distributions and their relationship to general distributions, J. Multivariate Anal., 148, 107-199 (2016) · Zbl 1338.62047
[98] Kim, H.-M.; Genton, M. G., Characteristic functions of scale mixtures of multivariate skew-normal distributions, J. Multivariate Anal., 102, 1105-1117 (2011) · Zbl 1221.60020
[99] Kim, H.-M.; Mallick, B. K., A Bayesian prediction using the skew Gaussian distribution, J. Statist. Plann. Inference, 120, 85-101 (2004) · Zbl 1038.62027
[100] Labra, F. V.; Garay, A. M.; Lachos, V. H.; Ortega, E. M.M., Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions, J. Statist. Plann. Inference, 142, 2149-2165 (2012) · Zbl 1408.62123
[101] Lachos, V. H.; Ghosh, P.; Arellano-Valle, R. B., Likelihood based inference for skew-normal independent linear mixed models, Statist. Sinica, 20, 303-322 (2010) · Zbl 1186.62071
[102] Lachos, V. H.; Moreno, E. J.L.; Chen, K.; Cabral, C. R.B., Finite mixture modeling of censored data using the multivariate Student-\(t\) distribution, J. Multivariate Anal., 159 (2017) · Zbl 1397.62221
[103] Lee, S.; Genton, M. G.; Arellano-Valle, R. B., Perturbation of numerical confidential data via skew-\(t\) distributions, Manage. Sci., 56, 318-333 (2010) · Zbl 1232.65009
[104] Lee, S.; McLachlan, G. J., Finite mixtures of multivariate skew \(t\)-distributions: some recent and new results, Stat. Comput., 24, 181-202 (2014), Available online 20 October 2012 · Zbl 1325.62107
[105] Lee, S. X.; McLachlan, G. J., Finite mixtures of canonical fundamental skew \(t\)-distributions, Stat. Comput., 26, 573-596 (2016), Available online 28 February 2015 · Zbl 1420.60020
[106] Lee, S. X.; McLachlan, G. J., EMMIXcskew: an R package for the fitting of a mixture of canonical fundamental skew \(t\)-distributions, J. Stat. Softw., Article 3 pp. (2018)
[107] Ley, C.; Verdebout, T., Skew-rotationally-symmetric distributions and related efficient inferential procedures, J. Multivariate Anal., 159, 67-81 (2017) · Zbl 1368.62134
[108] Lin, T. I., Maximum likelihood estimation for multivariate skew normal mixture models, J. Multivariate Anal., 100, 257-265 (2009) · Zbl 1152.62034
[109] Lin, T.-I.; Ho, H. J.; Chen, C. L., Analysis of multivariate skew normal models with incomplete data, J. Multivariate Anal., 100, 2337-2351 (2009) · Zbl 1175.62054
[110] Lin, T. I.; Lee, J. C.; Yen, S. Y., Finite mixture modelling using the skew normal distribution, Statist. Sinica, 17, 909-927 (2007) · Zbl 1133.62012
[111] Liseo, B., La classe delle densità normali sghembe: aspetti inferenziali da un punto di vista Bayesiano, Statistica L, 59-70 (1990)
[112] Liseo, B.; Loperfido, N., A Bayesian interpretation of the multivariate skew-normal distribution, Statist. Probab. Lett., 61, 395-401 (2003) · Zbl 1101.62342
[113] Liu, M.; Lin, T.-I., A skew-normal mixture regression model, Educ. Psychol. Meas., 74, 139-162 (2014), Available online 01 August 2013
[114] Ma, Y.; Genton, M. G., Flexible class of skew-symmetric distributions, Scand. J. Stat., 31, 459-468 (2004) · Zbl 1063.62079
[115] Ma, Y.; Genton, M. G.; Tsiatis, A. A., Locally efficient semiparametric estimators for generalized skew-elliptical distributions, J. Amer. Statist. Assoc., 100, 980-989 (2005) · Zbl 1117.62394
[116] Marchenko, Y. V.; Genton, M. G., A suite of commands for fitting the skew-normal and skew-\(t\) models, Stata J., 10, 507-539 (2010)
[117] Marchenko, Y. V.; Genton, M. G., A Heckman selection-\(t\) model, J. Amer. Statist. Assoc., 107, 304-317 (2012) · Zbl 1328.62429
[118] Mateu-Figueras, G.; Pawlowsky-Glahn, V., The skew-normal distribution on the simplex, Commun. Stat. Theory Methods, 36, 1787-1802 (2007) · Zbl 1315.60023
[119] Mattos, T.d.; M. Garay, A.; Lachos, V. H., Likelihood-based inference for censored linear regression models with scale mixtures of skew-normal distributions, J. Appl. Stat., 45, 2039-2066 (2018), Available online 02 December 2017
[120] Minozzo, M.; Bagnato, L., A unified skew-normal geostatistical factor model, Environmetrics, 32, Article e2672 pp. (2021)
[121] Minozzo, M.; Ferracuti, L., On the existence of some skew-normal stationary processes, Chil. J. Stat., 3, 159-172 (2012)
[122] Montenegro, L. C.; Lachos, V. H.; Bolfarine, H., Local influence analysis for skew-normal linear mixed models, Commun. Stat. Theory Methods, 38, 484-496 (2009) · Zbl 1159.62050
[123] Morris, S. A.; Reich, B. J.; Thibaud, E.; Cooley, D., A space-time skew-\(t\) model for threshold exceedances, Biometrics, 73, 749-758 (2017)
[124] Nelson, L. S., The sum of values from a normal and a truncated normal distribution, Technometrics, 6, 469-471 (1964)
[125] O’Hagan, A.; Leonard, T., Bayes estimation subject to uncertainty about parameter constraints, Biometrika, 63, 201-202 (1976) · Zbl 0326.62025
[126] Padoan, S. A., Multivariate extreme models based on underlying skew-\(t\) and skew-normal distributions, J. Multivariate Anal., 102, 977-991 (2011), Corrigendum at 143 (2016) 503 · Zbl 1233.62111
[127] Pewsey, A., The wrapped skew-normal distribution on the circle, Commun. Stat. Theory Methods, 29, 2459-2472 (2000) · Zbl 0992.62048
[128] Pewsey, A., Modelling asymmetrically distributed circular data using the wrapped skew-normal distribution, Environ. Ecol. Stat., 13, 257-269 (2006)
[129] Pourahmadi, M., Skew-normal ARMA models with nonlinear heteroscedastic predictors, Commun. Stat. Theory Methods, 36, 1803-1819 (2007) · Zbl 1315.62073
[130] Prates, M.; Lachos, V.; Cabral, C., The R package : Fitting finite mixture of scale mixture of skew-normal distributions (version 1.1-9) (2021), https://cran.r-project.org/package=mixsmsn
[131] Pretorious, S. J., Skew bivariate frequency surfaces, examined in the light of numerical illustrations, Biometrika, 22, 109-223 (1930) · JFM 56.1107.04
[132] Pyne, S.; Hu, X.; Wang, K.; Rossin, E.; Lin, T.-I.; Maier, L. M.; Baecher-Alland, C.; McLachlan, G. J.; Tamayo, P.; Hafler, D. A.; De Jagera, P. L.; Mesirov, J. P., Automated high-dimensional flow cytometric data analysis, Proc. Natl. Acad. Sci. USA, 106, 8519-8524 (2009)
[133] Roberts, C., A correlation model useful in the study of twins, J. Amer. Statist. Assoc., 61, 1184-1190 (1966) · Zbl 0147.38001
[134] Rotnitzky, A.; Cox, D. R.; Bottai, M.; Robbins, J., Likelihood-based inference with singular information matrix, Bernoulli, 6, 243-284 (2000) · Zbl 0976.62015
[135] Sahu, K.; Dey, D. K.; Branco, M. D., A new class of multivariate skew distributions with applications to Bayesian regression models, Canad. J. Stat., 31, 129-150 (2003), Corrigendum: 37 (2009) 301-302 · Zbl 1039.62047
[136] Sartori, N., Bias prevention of maximum likelihood estimates for scalar skew normal and skew \(t\) distributions, J. Statist. Plann. Inference, 136, 4259-4275 (2006) · Zbl 1098.62023
[137] Schumacher, F. L.; Lachos, V. H.; Matos, L. A., Scale mixture of skew-normal linear mixed models with within-subject serial dependence, Stat. Med. (2021)
[138] Schumacher, F. L.; Matos, L. A.; Lachos, V. H., The R package : Scale mixture of skew-normal linear mixed models (version 0.2.3) (2021), https://cran.r-project.org/package=skewlmm
[139] Tagle, F.; Castruccio, S.; Genton, M. G., A hierarchical bi-resolution spatial skew-\(t\) model, Spatial Stat., 35, Article 100398 pp. (2020), Available online 9 December 2019
[140] Tagle, F.; Genton, M. G.; Yip, A.; Mostamandi, S.; Stenchikov, G.; Castruccio, S., A high-resolution bilevel skew-\(t\) stochastic generator for assessing Saudi Arabia’s wind energy resources (with discussion), Environmetrics, 31, Article e2628 pp. (2020)
[141] Umbach, D.; Jammalamadaka, S. R., Building asymmetry into circular distributions, Statist. Probab. Lett., 79, 659-663 (2009) · Zbl 1156.62042
[142] Umbach, D.; Jammalamadaka, S. R., Some moment properties of skew-symmetric circular distributions, Metron, LXVIII, 265-273 (2010) · Zbl 1301.62025
[143] Vrbik, I.; McNicholas, P., Analytic calculations for the EM algorithm for multivariate skew \(t\)-mixture model, Statist. Probab. Lett., 82, 1169-1174 (2012) · Zbl 1244.65012
[144] Wallace, M. L.; Buysse, D. J.; Germain, A.; Hall, M. H.; Iyengar, S., Variable selection for skewed model-based clustering: application to the identification of novel sleep phenotypes, J. Amer. Statist. Assoc., 113, 95-110 (2018), Available online 26 June 2017 · Zbl 1398.62347
[145] Wang, J.; Boyer, J.; Genton, M. G., A skew-symmetric representation of multivariate distributions, Statist. Sinica, 14, 1259-1270 (2004) · Zbl 1060.62059
[146] Wang, S.; Zimmerman, D. L.; Breheny, P., Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew-\(t\) distributions, J. Multivariate Anal., 179 (2020) · Zbl 1448.62077
[147] Xie, F.-C.; Wei, B.-C.; Lin, J.-G., Homogeneity diagnostics for skew-normal nonlinear regression models, Statist. Probab. Lett., 79, 821-827 (2009) · Zbl 1157.62044
[148] Zareifard, H.; Jafari Khaledi, M., Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process, J. Multivariate Anal., 114, 16-28 (2013) · Zbl 1255.62303
[149] Zareifard, H.; Rue, H.; Khaledi, M. J.; Lindgren, F., A skew Gaussian decomposable graphical model, J. Multivariate Anal., 145, 58-72 (2016), Available online 28 August 2015 · Zbl 1331.62280
[150] Zeller, C. B.; Cabral, C. R.B.; Lachos, V. H., Robust mixture regression modeling based on scale mixtures of skew-normal distributions, Test, 25, 375-396 (2016), Available online 19 July 2015 · Zbl 1342.62113
[151] Zhang, H.; El-Shaarawi, A., On spatial skew-Gaussian processes and applications, Environmetrics, 21, 33-47 (2010), Available online 17 March 2009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.