Article
Full entry |
PDF
(0.7 MB)
Feedback
PDF
(0.7 MB)
Feedback
Keywords:
selection distribution; skew-normal; Gaussian copula
selection distribution; skew-normal; Gaussian copula
Summary:
Assuming that $C_{X,Y}$ is the copula function of $X$ and $Y$ with marginal distribution functions $F_{X}(x)$ and $F_{Y}(y)$, in this work we study the selection distribution $Z \overset{\mathrm{d}}{=}( X|Y \in T)$. We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.
References:
[1] Aigner, D., Lovell, C. A., Schmidt, P.: Formulation and estimation of stochastic frontier production function models. J. Econometrics 6 (1977), 21-37. DOI | MR 0448782
[2] Anděl, J., Netuka, I., Zvára, K.: On threshold autoregressive processes. Kybernetika 20 (1984), 89-106. DOI | MR 0747062
[3] Arnold, B. C., Beaver, R. J., Azzalini, A., Balakrishnan, N., Bhaumik, A., Dey, D. K., Cuadras, C. M., Sarabia, J.: Skewed multivariate models related to hidden truncation and/or selective reporting. Test 11 (2002), 7-54. DOI 10.1007/BF02595728 | MR 1915776
[4] Azzalini, A.: A class of distributions which includes the normal ones. Scand. J. Statist. (1985), 171-178. MR 0808153
[5] Azzalini, A., Capitanio, A.: Statistical applications of the multivariate skew-normal distribution. J. Royal Statist. Soc.: Series B, Statist. Methodology 61 (1999), 579-602. DOI | MR 1707862
[6] Azzalini, A., Valle, A. D.: The multivariate skew-normal distribution. Biometrika 83 (1996), 715-726. DOI | MR 1440039
[7] Cook, R. D., Weisberg, S.: An Introduction to Regression Graphics. John Wiley and Sons, 2009. MR 1285353
[8] Durante, F., Sempi, C.: Principles of Copula Theory. CRC Press, 2015. MR 3443023
[9] Harry, J.: Multivariate Models and Multivariate Dependence Concepts. CRC Press, 1997. MR 1462613
[10] Loperfido, N.: Modeling maxima of longitudinal contralateral observations. Test 17 (2008), 370-380. DOI | MR 2434333
[11] Roberts, C.: A correlation model useful in the study of twins. J. Amer. Statist. Assoc. 61 (1966), 1184-1190. DOI | MR 0205374
[12] Nelsen, R. B: An Introduction to Copulas. Springer Science and Business Media, 2006. MR 2197664 | Zbl 1152.62030
[13] Sheikhi, A., tata, M.: The exact joint distribution of concomitants of order statistics and their order statistics under normality. REVSTAT - Statistical Journal 11 (2013), 121-134. MR 3072467
[14] Sklar, A.: Fonctions de répartition an dimensions et leurs marges. Publ. inst. statist. univ. Paris 8 (1959), 229-231. MR 0125600
[15] Wang, J., Boyer, J., Genton, M. G.: A skew-symmetric representation of multivariate distributions. JSTOR, Statistica Sinica (2004), 1259-1270. MR 2126352
[16] Ždímalová, M., Chatterjee, A., Kosnáčová, H., Ghosh, M., Obaidullah, Sk., Kopáni, M., Kosnáč, D.: Various approaches to the quantitative evaluation of biological and medical data using mathematical models. Symmetry 14 (2021), 7. DOI
Search
Partner of
