메뉴 건너뛰기




Volumn 113, Issue , 2013, Pages 19-36

The distribution of the product of powers of independent uniform random variables - A simple but useful tool to address and better understand the structure of some distributions

Author keywords

Equality of mean vectors; Exponentiated Generalized Integer Gamma distribution; Generalized Integer Gamma distribution; Product of independent Beta random variables; Testing circularity; Testing equality of mean vectors and circularity; Wilks Lambda statistic

Indexed keywords


EID: 84867736231     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2011.04.006     Document Type: Article
Times cited : (20)

References (20)
  • 2
    • 0000181629 scopus 로고
    • Inference in multivariate elliptically contoured distributions based on maximum likelihood
    • K.-T. Fang, T.W. Anderson (Eds.)
    • Anderson T.W., Fang K.-T. Inference in multivariate elliptically contoured distributions based on maximum likelihood. Statistical Inference in Elliptically Contoured and Related Distributions 1990, 201-216. K.-T. Fang, T.W. Anderson (Eds.).
    • (1990) Statistical Inference in Elliptically Contoured and Related Distributions , pp. 201-216
    • Anderson, T.W.1    Fang, K.-T.2
  • 3
    • 84988123063 scopus 로고
    • Maximum-likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions
    • Anderson T.W., Fang K.-T., Hsu H. Maximum-likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions. Canad. J. Statist. 1986, 14:55-59.
    • (1986) Canad. J. Statist. , vol.14 , pp. 55-59
    • Anderson, T.W.1    Fang, K.-T.2    Hsu, H.3
  • 4
    • 0004231080 scopus 로고
    • International Cooperative Publ. House, Fairland, MD
    • Arnold B.C. Pareto Distributions 1983, International Cooperative Publ. House, Fairland, MD.
    • (1983) Pareto Distributions
    • Arnold, B.C.1
  • 5
    • 0040086381 scopus 로고    scopus 로고
    • The generalized integer gamma distribution-a basis for distributions in multivariate statistics
    • Coelho C.A. The generalized integer gamma distribution-a basis for distributions in multivariate statistics. J. Multivariate Anal. 1998, 64:86-102.
    • (1998) J. Multivariate Anal. , vol.64 , pp. 86-102
    • Coelho, C.A.1
  • 6
    • 84867695575 scopus 로고    scopus 로고
    • The exact and near-exact distributions of the product of independent beta random variables whose second parameter is rational
    • Coelho C.A. The exact and near-exact distributions of the product of independent beta random variables whose second parameter is rational. J. Combin. Inform. System Sci. 2006, 31:21-44.
    • (2006) J. Combin. Inform. System Sci. , vol.31 , pp. 21-44
    • Coelho, C.A.1
  • 7
    • 0006291137 scopus 로고
    • Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions
    • Fang C., Krishnaiah P.R., Nagarsenker B.N. Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions. J. Multivariate Anal. 1982, 12:597-611.
    • (1982) J. Multivariate Anal. , vol.12 , pp. 597-611
    • Fang, C.1    Krishnaiah, P.R.2    Nagarsenker, B.N.3
  • 8
    • 0001013602 scopus 로고
    • Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction)
    • Goodman N.R. Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). Ann. Math. Statist. 1963, 34:152-177.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 152-177
    • Goodman, N.R.1
  • 9
    • 0001240616 scopus 로고
    • The distribution of the determinant of a complex Wishart distributed matrix
    • Goodman N.R. The distribution of the determinant of a complex Wishart distributed matrix. Ann. Math. Statist. 1963, 34:178-180.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 178-180
    • Goodman, N.R.1
  • 10
    • 1642500767 scopus 로고
    • Invariant distributions associated with matrix laws under structural symmetry
    • Jensen D.R., Good I.J. Invariant distributions associated with matrix laws under structural symmetry. J. R. Stat. Soc. Ser. B Stat. Methodol. 1981, 43:327-332.
    • (1981) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.43 , pp. 327-332
    • Jensen, D.R.1    Good, I.J.2
  • 11
    • 0000173761 scopus 로고
    • Robustness of multivariate tests
    • Kariya T. Robustness of multivariate tests. Ann. Statist. 1981, 9:1267-1275.
    • (1981) Ann. Statist. , vol.9 , pp. 1267-1275
    • Kariya, T.1
  • 12
    • 0002227956 scopus 로고
    • Classical statistical analysis based on a certain multivariate complex Gaussian distribution
    • Khatri C.G. Classical statistical analysis based on a certain multivariate complex Gaussian distribution. Ann. Math. Statist. 1965, 36:98-114.
    • (1965) Ann. Math. Statist. , vol.36 , pp. 98-114
    • Khatri, C.G.1
  • 13
    • 0017150904 scopus 로고
    • The distributions of the likelihood ratio statistics for tests of certain covariance structures of complex multivariate normal populations
    • Krishnaiah P.R., Lee J.C., Chang T.C. The distributions of the likelihood ratio statistics for tests of certain covariance structures of complex multivariate normal populations. Biometrika 1976, 63:543-549.
    • (1976) Biometrika , vol.63 , pp. 543-549
    • Krishnaiah, P.R.1    Lee, J.C.2    Chang, T.C.3
  • 14
    • 79955784230 scopus 로고    scopus 로고
    • A general near-exact distribution theory for the most common likelihood ratio test statistics used in multivariate analysis
    • Marques F.J., Coelho C.A., Arnold B.C. A general near-exact distribution theory for the most common likelihood ratio test statistics used in multivariate analysis. Test 2010, 20:180-203.
    • (2010) Test , vol.20 , pp. 180-203
    • Marques, F.J.1    Coelho, C.A.2    Arnold, B.C.3
  • 15
    • 4544361208 scopus 로고    scopus 로고
    • Distribution and percentage points of the likelihood ratio statistic for testing circular symmetry
    • Nagar D.K., Chen J., Gupta A.K. Distribution and percentage points of the likelihood ratio statistic for testing circular symmetry. Comput. Statist. Data Anal. 2004, 47:79-89.
    • (2004) Comput. Statist. Data Anal. , vol.47 , pp. 79-89
    • Nagar, D.K.1    Chen, J.2    Gupta, A.K.3
  • 16
    • 0039065462 scopus 로고
    • Testing and estimation for a circular stationary model
    • Olkin I., Press S.J. Testing and estimation for a circular stationary model. Ann. Math. Statist. 1969, 40:1358-1373.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 1358-1373
    • Olkin, I.1    Press, S.J.2
  • 17
    • 0014797049 scopus 로고
    • The distribution of products of beta, gamma and Gaussian random variables
    • Springer M.D., Thompson W.E. The distribution of products of beta, gamma and Gaussian random variables. SIAM J. Appl. Meth. 1970, 18:721-737.
    • (1970) SIAM J. Appl. Meth. , vol.18 , pp. 721-737
    • Springer, M.D.1    Thompson, W.E.2
  • 19
    • 26944495864 scopus 로고
    • On the distribution of Wilks' statistic for testing the independence of several groups of variates
    • Wald A., Brookner R.J. On the distribution of Wilks' statistic for testing the independence of several groups of variates. Ann. Math. Statist. 1941, 12:137-152.
    • (1941) Ann. Math. Statist. , vol.12 , pp. 137-152
    • Wald, A.1    Brookner, R.J.2
  • 20
    • 0001537526 scopus 로고
    • The multivariate distribution of complex normal variables
    • Wooding R.A. The multivariate distribution of complex normal variables. Biometrika 1956, 43:212-215.
    • (1956) Biometrika , vol.43 , pp. 212-215
    • Wooding, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.