메뉴 건너뛰기




Volumn 139, Issue 11, 2009, Pages 3799-3819

Order statistics from trivariate normal and tν-distributions in terms of generalized skew-normal and skew-tν distributions

Author keywords

Bivariate t distribution; Generalized skew normal distribution; Generalized skew t distribution; Mixture distribution; Moment generating function; Multivariate t distribution; Order statistics; Orthant probabilities; Unified multivariate skew elliptical distribution; Unified multivariate skew normal distribution

Indexed keywords


EID: 68049086631     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2009.05.018     Document Type: Article
Times cited : (16)

References (41)
  • 1
    • 34547253275 scopus 로고    scopus 로고
    • Extensions of Stein's lemma for the skew-normal distribution
    • Adcock C.J. Extensions of Stein's lemma for the skew-normal distribution. Comm. Statist. Theory Methods 36 (2007) 1661-1671
    • (2007) Comm. Statist. Theory Methods , vol.36 , pp. 1661-1671
    • Adcock, C.J.1
  • 2
    • 33847711934 scopus 로고    scopus 로고
    • On the unification of families of skew-normal distributions
    • Arellano-Valle R.B., and Azzalini A. On the unification of families of skew-normal distributions. Scand. J. Statist. 33 (2006) 561-574
    • (2006) Scand. J. Statist. , vol.33 , pp. 561-574
    • Arellano-Valle, R.B.1    Azzalini, A.2
  • 4
    • 35349015206 scopus 로고    scopus 로고
    • On the exact distribution of linear combinations of order statistics from dependent random variables
    • Arellano-Valle R.B., and Genton M.G. On the exact distribution of linear combinations of order statistics from dependent random variables. J. Multivariate Anal. 98 (2007) 1876-1894
    • (2007) J. Multivariate Anal. , vol.98 , pp. 1876-1894
    • Arellano-Valle, R.B.1    Genton, M.G.2
  • 5
    • 36148943232 scopus 로고    scopus 로고
    • On the exact distribution of the maximum of absolutely dependent random variables
    • Arellano-Valle R.B., and Genton M.G. On the exact distribution of the maximum of absolutely dependent random variables. Statist. Probab. Lett. 78 (2008) 27-35
    • (2008) Statist. Probab. Lett. , vol.78 , pp. 27-35
    • Arellano-Valle, R.B.1    Genton, M.G.2
  • 7
    • 0036619050 scopus 로고    scopus 로고
    • Skew multivariate models related to hidden truncation and/or selective reporting
    • Arnold B.C., and Beaver R.J. Skew multivariate models related to hidden truncation and/or selective reporting. Test 11 (2002) 7-54
    • (2002) Test , vol.11 , pp. 7-54
    • Arnold, B.C.1    Beaver, R.J.2
  • 8
    • 0001036819 scopus 로고
    • A class of distributions which includes the normal ones
    • Azzalini A. A class of distributions which includes the normal ones. Scand. Actuar. J. 12 (1985) 171-178
    • (1985) Scand. Actuar. J. , vol.12 , pp. 171-178
    • Azzalini, A.1
  • 9
    • 0001611066 scopus 로고
    • Further results on a class of distributions which includes the normal ones
    • Azzalini A. Further results on a class of distributions which includes the normal ones. Statistica 46 (1986) 199-208
    • (1986) Statistica , vol.46 , pp. 199-208
    • Azzalini, A.1
  • 10
    • 19744373319 scopus 로고    scopus 로고
    • The skew-normal distribution and related multivariate families
    • Azzalini A. The skew-normal distribution and related multivariate families. Scand. J. Statist. 32 (2005) 159-188
    • (2005) Scand. J. Statist. , vol.32 , pp. 159-188
    • Azzalini, A.1
  • 11
    • 0037900005 scopus 로고    scopus 로고
    • Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution
    • Azzalini A., and Capitanio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65 (2003) 367-389
    • (2003) J. Roy. Statist. Soc. Ser. B , vol.65 , pp. 367-389
    • Azzalini, A.1    Capitanio, A.2
  • 12
    • 34248173389 scopus 로고    scopus 로고
    • Some results on the stress-strength model for skew normal variate
    • Azzalini, A., Chiogna, M., 2004. Some results on the stress-strength model for skew normal variate. Metron LXII, 315-326.
    • (2004) Metron , vol.62 , pp. 315-326
    • Azzalini, A.1    Chiogna, M.2
  • 13
    • 0001417140 scopus 로고    scopus 로고
    • The multivariate skew-normal distribution
    • Azzalini A., and Dalla Valle A. The multivariate skew-normal distribution. Biometrika 83 (1996) 715-726
    • (1996) Biometrika , vol.83 , pp. 715-726
    • Azzalini, A.1    Dalla Valle, A.2
  • 14
    • 43949165599 scopus 로고
    • Multivariate normal distribution and multivariate order statistics induced by ordering linear combinations
    • Balakrishnan N. Multivariate normal distribution and multivariate order statistics induced by ordering linear combinations. Statist. Probab. Lett. 17 (1993) 343-350
    • (1993) Statist. Probab. Lett. , vol.17 , pp. 343-350
    • Balakrishnan, N.1
  • 15
    • 68049088864 scopus 로고    scopus 로고
    • Balakrishnan, N., 2002. Discussion on Skew multivariate models related to hidden truncation and/or selective reporting by B.C. Arnold and R.J. Beaver. Test 11, 37-39.
    • Balakrishnan, N., 2002. Discussion on "Skew multivariate models related to hidden truncation and/or selective reporting" by B.C. Arnold and R.J. Beaver. Test 11, 37-39.
  • 16
    • 0000463734 scopus 로고
    • Identifiability of the multinormal and other distributions under competing risks model
    • Basu A.P., and Ghosh J.K. Identifiability of the multinormal and other distributions under competing risks model. J. Multivariate Anal. 8 (1978) 413-429
    • (1978) J. Multivariate Anal. , vol.8 , pp. 413-429
    • Basu, A.P.1    Ghosh, J.K.2
  • 18
    • 0035178888 scopus 로고    scopus 로고
    • A general class of multivariate elliptical distribution
    • Branco M., and Dey D.K. A general class of multivariate elliptical distribution. J. Multivariate Anal. 79 (2001) 99-113
    • (2001) J. Multivariate Anal. , vol.79 , pp. 99-113
    • Branco, M.1    Dey, D.K.2
  • 19
    • 21344495323 scopus 로고
    • The moment-generating function of the minimum of bivariate normal random variables
    • Cain M. The moment-generating function of the minimum of bivariate normal random variables. Amer. Statist. 48 (1994) 124-125
    • (1994) Amer. Statist. , vol.48 , pp. 124-125
    • Cain, M.1
  • 20
    • 34250207645 scopus 로고
    • Moments of the minimum of bivariate normal random variables
    • Cain M., and Pan E. Moments of the minimum of bivariate normal random variables. Math. Sci. 20 (1995) 119-122
    • (1995) Math. Sci. , vol.20 , pp. 119-122
    • Cain, M.1    Pan, E.2
  • 21
    • 0000244379 scopus 로고
    • On the theory of elliptically contoured distributions
    • Cambanis S., Huang S., and Simons G. On the theory of elliptically contoured distributions. J. Multivariate Anal. 11 (1981) 368-385
    • (1981) J. Multivariate Anal. , vol.11 , pp. 368-385
    • Cambanis, S.1    Huang, S.2    Simons, G.3
  • 22
    • 0010344639 scopus 로고    scopus 로고
    • Some results on the scalar skew-normal distribution
    • Chiogna M. Some results on the scalar skew-normal distribution. J. Italian Statist. Soc. 7 (1998) 1-13
    • (1998) J. Italian Statist. Soc. , vol.7 , pp. 1-13
    • Chiogna, M.1
  • 23
    • 0042779441 scopus 로고
    • Recurrence relations between moments of order statistics for exchangeable variates
    • David H.A., and Joshi P.C. Recurrence relations between moments of order statistics for exchangeable variates. Ann. Math. Statist. 39 (1968) 272-274
    • (1968) Ann. Math. Statist. , vol.39 , pp. 272-274
    • David, H.A.1    Joshi, P.C.2
  • 27
    • 0001205992 scopus 로고
    • Probability integrals of multivariate normal and multivariate t
    • Gupta S.S. Probability integrals of multivariate normal and multivariate t. Ann. Math. Statist. 34 (1963) 792-828
    • (1963) Ann. Math. Statist. , vol.34 , pp. 792-828
    • Gupta, S.S.1
  • 28
    • 85041932706 scopus 로고
    • On the order statistics from equally correlated normal random variables
    • Gupta S.S., Nagel K., and Panchapakesan S. On the order statistics from equally correlated normal random variables. Biometrika 60 (1973) 403-413
    • (1973) Biometrika , vol.60 , pp. 403-413
    • Gupta, S.S.1    Nagel, K.2    Panchapakesan, S.3
  • 29
    • 33745369429 scopus 로고
    • On linear functions of ordered correlated normal random variables
    • Gupta S.S., and Pillai K.C.S. On linear functions of ordered correlated normal random variables. Biometrika 52 (1965) 367-379
    • (1965) Biometrika , vol.52 , pp. 367-379
    • Gupta, S.S.1    Pillai, K.C.S.2
  • 30
    • 0000811912 scopus 로고
    • A probabilistic representation of the skew-normal distribution
    • Henze N.A. A probabilistic representation of the skew-normal distribution. Scand. J. Statist. 13 (1986) 271-275
    • (1986) Scand. J. Statist. , vol.13 , pp. 271-275
    • Henze, N.A.1
  • 31
    • 0006288770 scopus 로고
    • A note on strong unimodality of order statistics
    • Huang J.S., and Ghosh M. A note on strong unimodality of order statistics. J. Amer. Statist. Assoc. 77 (1982) 929-930
    • (1982) J. Amer. Statist. Assoc. , vol.77 , pp. 929-930
    • Huang, J.S.1    Ghosh, M.2
  • 33
    • 58549092964 scopus 로고    scopus 로고
    • Recurrence relations for distributions of skew-t and a linear combination of order statistics from a bivariate-t
    • Jamalizadeh, A., Khosravi, M., Balakrishnan, N., 2009. Recurrence relations for distributions of skew-t and a linear combination of order statistics from a bivariate-t. Comput. Statist. Data Anal. 53, 847-852.
    • (2009) Comput. Statist. Data Anal , vol.53 , pp. 847-852
    • Jamalizadeh, A.1    Khosravi, M.2    Balakrishnan, N.3
  • 34
  • 35
    • 0004167764 scopus 로고
    • Stanford University Press, Stanford
    • Karlin S. Total Positivity vol. 1 (1968), Stanford University Press, Stanford
    • (1968) Total Positivity , vol.1
    • Karlin, S.1
  • 37
    • 38249041823 scopus 로고
    • Moments of ordered bivariate log-normal distributions
    • Lien D.-H.D. Moments of ordered bivariate log-normal distributions. Econom. Lett. 20 (1986) 45-47
    • (1986) Econom. Lett. , vol.20 , pp. 45-47
    • Lien, D.-H.D.1
  • 38
    • 0037441768 scopus 로고    scopus 로고
    • A Bayesian interpretation of the multivariate skew-normal distribution
    • Liseo B., and Loperfido B. A Bayesian interpretation of the multivariate skew-normal distribution. Statist. Probab. Lett. 61 (2003) 396-401
    • (2003) Statist. Probab. Lett. , vol.61 , pp. 396-401
    • Liseo, B.1    Loperfido, B.2
  • 39
    • 0010299276 scopus 로고    scopus 로고
    • Quadratic forms of skew-normal random vectors
    • Loperfido N. Quadratic forms of skew-normal random vectors. Statist. Probab. Lett. 54 (2001) 381-387
    • (2001) Statist. Probab. Lett. , vol.54 , pp. 381-387
    • Loperfido, N.1
  • 40
    • 34547320472 scopus 로고
    • A note on linear functions of ordered correlated normal random variables
    • Nagaraja H.N. A note on linear functions of ordered correlated normal random variables. Biometrika 69 (1982) 284-285
    • (1982) Biometrika , vol.69 , pp. 284-285
    • Nagaraja, H.N.1
  • 41
    • 0014097055 scopus 로고
    • Recurrence relations between the P.D.F.'s of order statistics of dependent variables, and some applications
    • Young D.H. Recurrence relations between the P.D.F.'s of order statistics of dependent variables, and some applications. Biometrika 54 (1967) 283-292
    • (1967) Biometrika , vol.54 , pp. 283-292
    • Young, D.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.