| Title:
|
On asymmetric distributions of copula related random variables which includes the skew-normal ones (English) |
| Author:
|
Sheikhi, Ayyub |
| Author:
|
Arad, Fereshteh |
| Author:
|
Mesiar, Radko |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
58 |
| Issue:
|
6 |
| Year:
|
2022 |
| Pages:
|
984-995 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
selection distribution |
| Keyword:
|
skew-normal |
| Keyword:
|
Gaussian copula |
| MSC:
|
62Exx |
| MSC:
|
62H05 |
| idZBL:
|
Zbl 07655867 |
| idMR:
|
MR4548224 |
| DOI:
|
10.14736/kyb-2022-6-0984 |
| . |
| Date available:
|
2023-02-10T13:52:37Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151539 |
| . |
| Reference:
|
[1] Aigner, D., Lovell, C. A., Schmidt, P.: Formulation and estimation of stochastic frontier production function models..J. Econometrics 6 (1977), 21-37. MR 0448782, |
| Reference:
|
[2] Anděl, J., Netuka, I., Zvára, K.: On threshold autoregressive processes..Kybernetika 20 (1984), 89-106. MR 0747062, |
| Reference:
|
[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. MR 1915776, 10.1007/BF02595728 |
| Reference:
|
[4] Azzalini, A.: A class of distributions which includes the normal ones..Scand. J. Statist. (1985), 171-178. MR 0808153 |
| Reference:
|
[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. MR 1707862, |
| Reference:
|
[6] Azzalini, A., Valle, A. D.: The multivariate skew-normal distribution..Biometrika 83 (1996), 715-726. MR 1440039, |
| Reference:
|
[7] Cook, R. D., Weisberg, S.: An Introduction to Regression Graphics..John Wiley and Sons, 2009. MR 1285353 |
| Reference:
|
[8] Durante, F., Sempi, C.: Principles of Copula Theory..CRC Press, 2015. MR 3443023 |
| Reference:
|
[9] Harry, J.: Multivariate Models and Multivariate Dependence Concepts..CRC Press, 1997. MR 1462613 |
| Reference:
|
[10] Loperfido, N.: Modeling maxima of longitudinal contralateral observations..Test 17 (2008), 370-380. MR 2434333, |
| Reference:
|
[11] Roberts, C.: A correlation model useful in the study of twins..J. Amer. Statist. Assoc. 61 (1966), 1184-1190. MR 0205374, |
| Reference:
|
[12] Nelsen, R. B: An Introduction to Copulas..Springer Science and Business Media, 2006. Zbl 1152.62030, MR 2197664 |
| Reference:
|
[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 |
| Reference:
|
[14] Sklar, A.: Fonctions de répartition an dimensions et leurs marges..Publ. inst. statist. univ. Paris 8 (1959), 229-231. MR 0125600 |
| Reference:
|
[15] Wang, J., Boyer, J., Genton, M. G.: A skew-symmetric representation of multivariate distributions..JSTOR, Statistica Sinica (2004), 1259-1270. MR 2126352 |
| Reference:
|
[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. |
| . |
