On asymmetric distributions of copula related random variables which includes the skew-normal ones

Ayyub Sheikhi; Fereshteh Arad; Radko Mesiar

Kybernetika (2022)

  • Volume: 58, Issue: 6, page 984-995
  • ISSN: 0023-5954

Abstract

top
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 = d ( X | Y ∈ 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.

How to cite

top

Sheikhi, Ayyub, Arad, Fereshteh, and Mesiar, Radko. "On asymmetric distributions of copula related random variables which includes the skew-normal ones." Kybernetika 58.6 (2022): 984-995. <http://eudml.org/doc/299338>.

@article{Sheikhi2022,
abstract = {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.},
author = {Sheikhi, Ayyub, Arad, Fereshteh, Mesiar, Radko},
journal = {Kybernetika},
keywords = {selection distribution; skew-normal; Gaussian copula},
language = {eng},
number = {6},
pages = {984-995},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On asymmetric distributions of copula related random variables which includes the skew-normal ones},
url = {http://eudml.org/doc/299338},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Sheikhi, Ayyub
AU - Arad, Fereshteh
AU - Mesiar, Radko
TI - On asymmetric distributions of copula related random variables which includes the skew-normal ones
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 6
SP - 984
EP - 995
AB - 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.
LA - eng
KW - selection distribution; skew-normal; Gaussian copula
UR - http://eudml.org/doc/299338
ER -

References

top
  1. Aigner, D., Lovell, C. A., Schmidt, P., , J. Econometrics 6 (1977), 21-37. MR0448782DOI
  2. Anděl, J., Netuka, I., Zvára, K., , Kybernetika 20 (1984), 89-106. MR0747062DOI
  3. Arnold, B. C., Beaver, R. J., Azzalini, A., Balakrishnan, N., Bhaumik, A., Dey, D. K., Cuadras, C. M., Sarabia, J., 10.1007/BF02595728, Test 11 (2002), 7-54. MR1915776DOI10.1007/BF02595728
  4. Azzalini, A., A class of distributions which includes the normal ones., Scand. J. Statist. (1985), 171-178. MR0808153
  5. Azzalini, A., Capitanio, A., , J. Royal Statist. Soc.: Series B, Statist. Methodology 61 (1999), 579-602. MR1707862DOI
  6. Azzalini, A., Valle, A. D., , Biometrika 83 (1996), 715-726. MR1440039DOI
  7. Cook, R. D., Weisberg, S., An Introduction to Regression Graphics., John Wiley and Sons, 2009. MR1285353
  8. Durante, F., Sempi, C., Principles of Copula Theory., CRC Press, 2015. MR3443023
  9. Harry, J., Multivariate Models and Multivariate Dependence Concepts., CRC Press, 1997. MR1462613
  10. Loperfido, N., , Test 17 (2008), 370-380. MR2434333DOI
  11. Roberts, C., , J. Amer. Statist. Assoc. 61 (1966), 1184-1190. MR0205374DOI
  12. Nelsen, R. B, An Introduction to Copulas., Springer Science and Business Media, 2006. Zbl1152.62030MR2197664
  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. MR3072467
  14. Sklar, A., Fonctions de répartition an dimensions et leurs marges., Publ. inst. statist. univ. Paris 8 (1959), 229-231. MR0125600
  15. Wang, J., Boyer, J., Genton, M. G., A skew-symmetric representation of multivariate distributions., JSTOR, Statistica Sinica (2004), 1259-1270. MR2126352
  16. Ždímalová, M., Chatterjee, A., Kosnáčová, H., Ghosh, M., Obaidullah, Sk., Kopáni, M., Kosnáč, D., , Symmetry 14 (2021), 7. DOI

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.