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### Characterization of Some Classes of Distributions Related to Operator Semi-stable Distributions

Joo, Sang Yeol   (Department of Statistics, Kangwon National UniversityUU0000037  ); Yoo, Young Ho   (Department of Statistics, Kangwon National UniversityUU0000037  ); Choi, Gyeong Suk   (Department of Statistics, Kangwon National UniversityUU0000037  );

For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on R^d$are defined. The operator m-semi-stability is a generalization of the definition of operator semi-stability with exponent Q. Characterization of strictly operator na-semi-stable distributions among operator m-semi-stable distributions is given. Translation of strictly operator m-semi-stable distribution is discussed. • #### 주제어 Operator semi-stability . Semi-stability . Operator stability . Strictly semi-stability. • #### 참고문헌 (21) 1. Characterization of operator-semi-stable distributions , Chorny, V. , Mathematica Slovaca / v.39,pp.99-104, 2. English translation , Krapavickaite, D. , Lithuanian Math. J. / v.20,pp.298-303, 3. Linear forms and statistical criteria(in Russian) , Linnik, Y. , Ukrain. Math. Statist. and Pro. / v.5,pp.207-243;247-290, 4. Sato, K. , L$\'{e}$vy Processes and Infinitely Divisible Distributions / v.,pp., 5. Operator-stable probability distributions on vector groups , Sharpe, M. , Trans. Amer. Math. Soc. / v.136,pp.51-65, 6. Solution to a functional equation and its application to some characterization problem , Shimizu, R. , Sankhy a, Ser.A / v.40,pp.319-332, 7. Lectures on multivariate infinitely divisible distributions and operator-stable processes , Sato, K. , Technical Report Series, Lab.Res. Statist. Probab. Carleton Unvi. and Univ Ottawa / v.,pp., 8. English translation , Krapavickaite, D. , Lithuanian Math.J. / v.20,pp.111-118, 9. Characterization of strictly operator semi-stable distributions , Choi, G. S. , J. Korean Math. Soc. / v.38,pp.101-123, 10. Certain classes of probability distributions , Krapavickaite, D. , Litovsk. Mat. Sb. / v.20-4,pp.79-86, 11. General characterization theorems for the Weibull and stable distributions , Shimizu, R.;Davies, L. , Sankhy a, Ser.A / v.43,pp.282-310, 12. Completely operator-selfdecomposable distribut-ions and operator-stable distributions , Sato, K.;Yamazato, M. , Nagoya. Math. J. / v.97,pp.71-94, 13. Linnik, Y. , Selected Translations in Math. Statist. and Pro.(English translation) / v.3,pp.1-90, 14. Characteristic function satisfying a functional equation I , Shimizu, R. , Ann. Inst. Statist. Math. / v.20,pp.187-209, 15. L$\'{e}$vy, P. , Theorie de l'addition des variables aleatoires ($2^e$ed.) / v.,pp., 16. Representation of operator semi-stable distributions , Choi, G. S. , Bull. Korean Math. Soc. / v.37,pp.135-152, 17. Strictly operator-stable distributions , Sato, K. , J. Multivar. Anal. / v.22,pp.278-295, 18. Semi-stable probability measures on$R^N\$ , Jajte, R. , Studia Math. / v.61,pp.29-39,
19. Characterization of some classes of multidimensional distributions related to semi-stable distributions , Choi, G. S. , Japan. J. Math. / v.21,pp.335-353,
20. Generalized semistable probability distributions , Krapavickaite, D. , Litovsk.Mat.Sb. / v.20-2,pp.57-68,
21. Solution of functional equations arising in some regression problems and a characterizations the Cauchy law , Ramachandran, B.;Rao, C. R. , Sankhya, Ser. A / v.32,pp.1-30,

저자의 다른 논문

• #### Joo, Sang-Yeol (19)

1. 1999 "Limit Theorems for Fuzzy Martingales" Journal of the Korean Statistical Society 28 (1): 21~34
2. 2000 "On Designing a Distributed Management System with Reliability" International journal of reliability and applications 1 (2): 105~113
3. 2000 "Tests of Statistical Hypotheses for Gaussian Fuzzy Population" International journal of reliability and applications 1 (2): 145~154
4. 2001 "A Strong Law of Large Numbers for Stationary Fuzzy Random Variables" Journal of the Korean Statistical Society 30 (1): 153~161
5. 2001 "CONTINUITY OF THE ADDITION AND SCALAR MULTIPLICATION ON THE SPACE OF FUZZY SETS" The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A 8 (2): 551~560
6. 2002 "Characterization of Tightness for Fuzzy Random Variables" 한국통계학회 논문집 = Communications of the Korean Statistical Society 9 (3): 871~876
7. 2002 "Performance and Fairness Analyses of a STA/LTA based Internet Congestion Algorithm" International journal of reliability and applications 3 (2): 99~112
8. 2003 "TIGHTNESS OF LEVEL-WISE CONTINUOUS FUZZY RANDOM VARIABLES" Journal of the Korean Statistical Society 32 (1): 73~83
9. 2005 "퍼지 랜덤 집합에 대한 중심극한정리" 퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems 15 (3): 337~342
10. 2005 "Convergence in Probability for Weighted Sums of Fuzzy Random Variables" 한국통계학회 논문집 = Communications of the Korean Statistical Society 12 (2): 275~283

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