Infinite divisibility of skew Gaussian and Laplace laws

Statistics and Probability Letters

Volumn 78, Issue 6, 2008, Pages 654-660

  Kozubowski, Tomasz J ^a   Nolan, John P ^b  

^a UNIVERSITY OF NEVADA   (United States)

^b AMERICAN UNIVERSITY   (United States)

Author keywords

Asymmetric Laplace law; Class L; Infinite divisibility; Self decomposable law; Simulation; Skew double exponential model; Skew normal distribution; Two piece normal distribution

Indexed keywords

EID: 40749086097     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2007.09.027     Document Type: Article

References (36)

1. Aigner D.J., Lovell C.H.K., and Schmidt P. Formulation and estimation of stochastic frontier production function method. J. Econometrics 12 (1977) 21-37
2. Andel J., Netuka I., and Szara K. On the threshold autoregressive processes. Kybernetika 20 (1984) 89-106
3. Arnold B.C., and Beaver R.J. Skew multivariate models related to hidden truncation and/or selective reporting. Test 11 1 (2002) 7-54
4. Arnold B.C., Beaver R.J., Gorenveld R.A., and Meeker W.Q. The nontruncated marginal of a truncated bivariate normal distribution. Psychometrika 58 (1993) 471-478
5. Aryal G., and Nadarajah S. On the skew Laplace distribution. J. Inform. Optim. Sci. 26 1 (2005) 205-217
6. Azzalini A. A class of distributions which includes the normal ones. Scand. J. Statist. 12 (1985) 171-178
7. Azzalini A. Further results on a class of distributions which includes the normal ones. Statistica 46 (1986) 199-208
8. Azzalini A. The skew-normal distribution and related multivariate families. Scand. J. Statist. 32 (2005) 159-188
9. Azzalini A., and Capitanio A. Statistical applications of the multivariate skew normal distribution. J. Roy. Statist. Soc. Ser. B 3 (1999) 579-602
10. Azzalini A., and Dalla Valle A. The multivariate skew-normal distribution. Biometrika 83 (1996) 715-726
11. Domínguez-Molina, J.A., Rocha-Arteaga, A., 2004. A note on the infinite divisibility of skew-symmetric distributions. Communicacion Tecnica No. I-04-07/17-08.
12. Fechner G.T. Kollectivmasslehre (1897), Engleman, Leipzig
13. Fernández C., and Steel F.J. On Bayesian modeling of fat tails and skewness. J. Amer. Statist. Assoc. 93 (1998) 359-371
14. Genton M.G., He L., and Liu X. Moments of skew-normal random vectors and their quadratic forms. Statist. Probab. Lett. 51 (2001) 319-325
15. Gibbons J.F., and Mylroie S.W. Estimation of impurity profiles in ion-implanted amorphous targets using joined half-Gaussian distributions. Appl. Phys. Lett. 22 (1973) 568-569
16. Gibbons J.F., Johnson W.S., and Mylroie S.W. Projected Range Statistics: Semiconductors and Related Materials (1975), Halsted Press, New York
17. Gupta A.K., and Chen T. Goodness of fit tests for the skew normal distribution. Comm. Statist. Simulation Comput. 30 4 (2001) 907-930
18. Gupta A.K., and Chen T. On the sample characterization criterion for normal distributions. J. Statist. Comput. Simulation 73 3 (2003) 155-163
19. Gupta A.K., and Chen T. A class of multivariate skew-normal models. Ann. Inst. Statist. Math. 56 2 (2004) 305-315
20. Gupta A.K., and Huang W.J. Quadratic forms in skew normal variates. J. Math. Anal. Appl. 273 (2002) 558-564
21. Gupta A.K., Chang F.C., and Huang W.J. Some skew-symmetric models. Random Operations Stochastic Equations 10 2 (2002) 133-140
22. Gupta A.K., González-Farías G., and Domíngez-Molina J.A. A multivariate skew normal distribution. J. Multivariate Anal. 89 (2004) 181-190
23. Gupta A.K., Nguyen T.T., and Sanqui J.A.T. Characterization of the skew-normal distribution. Ann. Inst. Statist. Math. 56 2 (2004) 351-360
24. Henze N. A probabilistic representation of the 'skew-normal' distribution. Scand. J. Statist. 13 (1986) 271-275
25. Jagannathan, K., 2005. Statistical inference and goodness-of-fit tests for skewed double exponential models. Ph.D. Dissertation, Mathematics and Statistics, Bowling Green State University, OH.
26. John S. The three-parameter two-piece normal family of distributions and its fitting. Comm. Statist. Theory Methods 11 8 (1982) 879-885
27. Kimber A.C. Methods for the two-piece normal distribution. Comm. Statist. Theory Methods 14 1 (1985) 235-245
28. Kimber A.C., and Jeynes C. An application of the truncated two-piece normal distribution to the measurement of depths of arsenic implants in silicon. Appl. Statist. 36 (1987) 352-357
29. Kotz S., Kozubowski T.J., and Podgórski K. The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance (2001), Birkhaüser, Boston
30. Liseo B. The skew-normal class of densities: aspects of inference from the Bayesian point of view. Statistica 50 (1990) 71-82 (in Italian)
31. Lukacs, E., 1970. Characteristic Functions, second ed. Griffin, London.
32. Mudholkar G.S., and Hutson A.D. The epsilon-skew-normal distribution for analyzing near-normal data. J. Statist. Plann. Inference 83 (2000) 291-309
33. O'Hagan A., and Leonard T. Bayes estimation subject to uncertainty about parameter constrains. Biometrika 63 (1976) 201-203
34. Roberts C. A correlation model useful in the study of twins. J. Amer. Statist. Assoc. 61 (1966) 1184-1190
35. Steutel F.W., and van Harn K. Infinite Divisibility of Probability Distributions on the Real Line (2004), Marcel Dekker, New York
36. Toth Z., and Szentimrey T. The binormal distribution: a distribution for representing asymmetrical but normal-like weather elements. J. Climate 3 (1990) 128-136