Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
281-293
Opis fizyczny
Daty
wydano
2011-04-01
online
2011-02-18
Twórcy
autor
- Marie Curie-Skłodowska University, matula@hektor.umcs.lublin.pl
autor
- Marie Curie-Skłodowska University, maciek.ziemba@gmail.com
Bibliografia
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- [2] Bulinski A., Shashkin A., Limit Theorems for Associated Random Fields and Related Systems, Adv. Ser. Stat. Sci. Appl. Probab., 10, World Scientific, Hackensack, 2007
- [3] Cai Z., Roussas G.G., Smooth estimate of quantiles under association, Statist. Probab. Lett., 1997, 36(3), 275–287 http://dx.doi.org/10.1016/S0167-7152(97)00074-6
- [4] Chung K.L., A Course in Probability Theory, 3rd ed., Academic Press, San Diego, 2001
- [5] Etemadi N., Stability of sums of weighted nonnegative random variables, J. Multivariate Anal., 1983, 13, 361–365 http://dx.doi.org/10.1016/0047-259X(83)90032-5
- [6] Karlin S., Rinott Y., Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions, J. Multivariate Anal., 1980, 10(4), 467–498 http://dx.doi.org/10.1016/0047-259X(80)90065-2
- [7] Kotz S., Balakrishnan N., Johnson N.L., Continuous Multivariate Distributions, 2nd ed., Wiley Ser. Probab. Statist. Appl. Probab. Statist., Wiley, New York, 2000 http://dx.doi.org/10.1002/0471722065
- [8] Lehmann E.L., Some concepts of dependence, Ann. Math. Statist., 1966, 37(5), 1137–1153 http://dx.doi.org/10.1214/aoms/1177699260
- [9] Matuła P., On some inequalities for positively and negatively dependent random variables with applications, Publ. Math. Debrecen, 2003, 63(4), 511–522
- [10] Matuła P., A note on some inequalities for certain classes of positively dependent random variables, Probab. Math. Statist., 2004, 24(1), 17–26
- [11] Nelsen R.B., An Introduction to Copulas, 2nd ed., Springer Ser. Statist., Springer, New York, 2006
- [12] Newman C.M., Asymptotic independence and limit theorems for positively and negatively dependent random variables, In: Inequalities in Statistics and Probability, Lincoln, 1982, Inst Math. Statist., Hayward, 1984, 127–140 http://dx.doi.org/10.1214/lnms/1215465639
- [13] Rodríguez-Lallena J.A., Úbeda-Flores M., A new class of bivariate copulas, Statist. Probab. Lett., 2004, 66(3), 315–325 http://dx.doi.org/10.1016/j.spl.2003.09.010
- [14] Roussas G.G., Kernel estimates under association: strong uniform consistency, Statist. Probab. Lett., 1991, 12(5), 393–403 http://dx.doi.org/10.1016/0167-7152(91)90028-P
- [15] Schweizer B., Wolff E.F., On nonparametric measures of dependence for random variables, Ann. Statist., 1981, 9(4), 879–885 http://dx.doi.org/10.1214/aos/1176345528
- [16] Yu H., A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences, Probab. Theory Related Fields, 1993, 95(3), 357–370 http://dx.doi.org/10.1007/BF01192169
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0006-2