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Volumn 52, Issue 2, 2000, Pages 215-230

Moment-based approximations of distributions using mixtures: Theory and applications

Author keywords

Cumulants; Cumulative distribution function; Gamma mixtures; Mixture distribution; Moment matrix; p point mixture; Tail probability; Weighted sums of chi squares

Indexed keywords


EID: 6744255835     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004105603806     Document Type: Article
Times cited : (53)

References (23)
  • 1
    • 84985534899 scopus 로고
    • An approximation to the distribution of quadratic forms in normal random variables
    • Buckley, M. J. and Eagleson, G. K. (1988). An approximation to the distribution of quadratic forms in normal random variables, Austral. J. Statist., 30A, 150-159.
    • (1988) Austral. J. Statist. , vol.30 A , pp. 150-159
    • Buckley, M.J.1    Eagleson, G.K.2
  • 2
    • 0001008882 scopus 로고
    • The distribution of a linear combination of independent chi-squared random variables
    • Davies, R. B. (1980). The distribution of a linear combination of independent chi-squared random variables, Applied Statistics, 29, 323-333.
    • (1980) Applied Statistics , vol.29 , pp. 323-333
    • Davies, R.B.1
  • 3
    • 0041337277 scopus 로고
    • A differential equation approach to linear combinations of independent chi-squares
    • Davis, A. W. (1977). A differential equation approach to linear combinations of independent chi-squares, J. Amer. Statist. Assoc., 72, 212-214.
    • (1977) J. Amer. Statist. Assoc. , vol.72 , pp. 212-214
    • Davis, A.W.1
  • 4
    • 0041337276 scopus 로고
    • The distribution of positive linear combination of independent chi-squared random variables
    • Farebrother R. W. (1984). The distribution of positive linear combination of independent chi-squared random variables, Applied Statistics, 33, 332-339.
    • (1984) Applied Statistics , vol.33 , pp. 332-339
    • Farebrother, R.W.1
  • 5
    • 0004536780 scopus 로고
    • A quick and easy approximation to the distribution of a sum of weighted chi-square variables
    • Gabler, S. and Wolff, C. (1987). A quick and easy approximation to the distribution of a sum of weighted chi-square variables, Statistische Hefte, 28, 317-325.
    • (1987) Statistische Hefte , vol.28 , pp. 317-325
    • Gabler, S.1    Wolff, C.2
  • 6
    • 0041837905 scopus 로고
    • Chi-squared approximation to the distribution of a sum of independent random variables
    • Hall, P. (1983). Chi-squared approximation to the distribution of a sum of independent random variables, Ann. Probab., 11, 1028-1036.
    • (1983) Ann. Probab. , vol.11 , pp. 1028-1036
    • Hall, P.1
  • 7
    • 0001507590 scopus 로고
    • Computing the distribution of quadratic forms in normal variables
    • Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables, Biometrika, 48, 417-426.
    • (1961) Biometrika , vol.48 , pp. 417-426
    • Imhof, J.P.1
  • 8
    • 0000009877 scopus 로고
    • A Gaussian approximation to the distribution of a definite quadratic form
    • Jensen, D. R. and Solomon, H. (1972). A Gaussian approximation to the distribution of a definite quadratic form, J. Amer. Statist. Assoc., 67, 898-902.
    • (1972) J. Amer. Statist. Assoc. , vol.67 , pp. 898-902
    • Jensen, D.R.1    Solomon, H.2
  • 9
    • 0001544489 scopus 로고
    • On the determinants of moment matrices
    • Lindsay, B. G. (1989a). On the determinants of moment matrices, Ann. Statist, 17, 711-721.
    • (1989) Ann. Statist , vol.17 , pp. 711-721
    • Lindsay, B.G.1
  • 10
    • 0001402114 scopus 로고
    • Moment matrices: Applications in mixtures
    • Lindsay, B. G. (1989b). Moment matrices: Applications in mixtures, Ann. Statist., 17, 722-740.
    • (1989) Ann. Statist. , vol.17 , pp. 722-740
    • Lindsay, B.G.1
  • 11
    • 0042339044 scopus 로고
    • Moments determine the tail of a distribution (but not much else)
    • Center for Likelihood Studies, Department of Statistics, The Pennsylvania State University, University Park, PA
    • Lindsay, B. G. and Basak, P. (1995). Moments determine the tail of a distribution (but not much else), Tech. Report, No. 95-7, Center for Likelihood Studies, Department of Statistics, The Pennsylvania State University, University Park, PA.
    • (1995) Tech. Report , vol.95 , Issue.7
    • Lindsay, B.G.1    Basak, P.2
  • 12
    • 0031494309 scopus 로고    scopus 로고
    • Moment-based oscillation properties of mixture models
    • Lindsay, B. G. and Roeder, K. (1997). Moment-based oscillation properties of mixture models, Ann. Statist., 25, 378-386.
    • (1997) Ann. Statist. , vol.25 , pp. 378-386
    • Lindsay, B.G.1    Roeder, K.2
  • 13
    • 0041337275 scopus 로고
    • Moment-based approximations of distributions using mixtures: Theory and applications
    • Center for Likelihood Studies, Department of Statistics, The Pennsylvania State University, University Park, PA
    • Lindsay, B. G., Pilla, R. S. and Basak, P. (1995) Moment-based approximations of distributions using mixtures: theory and applications, Tech. Report, No. 95-9, Center for Likelihood Studies, Department of Statistics, The Pennsylvania State University, University Park, PA.
    • (1995) Tech. Report , vol.95 , Issue.9
    • Lindsay, B.G.1    Pilla, R.S.2    Basak, P.3
  • 14
    • 0041837909 scopus 로고
    • A mixture approximation to the distribution of a weighted sum of chi-squared variables
    • Oman, S. D. and Zacks, S. (1981). A mixture approximation to the distribution of a weighted sum of chi-squared variables, J. Statist. Comput. Simulation, 13, 215-224.
    • (1981) J. Statist. Comput. Simulation , vol.13 , pp. 215-224
    • Oman, S.D.1    Zacks, S.2
  • 15
    • 0041337270 scopus 로고
    • Department of Statistics, The Pennsylvania State University, University Park, PA-16802 (Program is available by sending an email to pillar@helix-nih-gov)
    • Pilla, R. S. (1995). Approximation Using Gamma Mixtures (AUGM): A special version of the FORTRAN program, Department of Statistics, The Pennsylvania State University, University Park, PA-16802 (Program is available by sending an email to pillar@helix-nih-gov).
    • (1995) Approximation Using Gamma Mixtures (AUGM): A Special Version of the FORTRAN Program
    • Pilla, R.S.1
  • 17
    • 0000989367 scopus 로고
    • Probability concent of regions under spherical distributions, IV: The distribution of homogeneous and non homogeneous quadratic functions of normal variables
    • Ruben, H. (1962). Probability concent of regions under spherical distributions, IV: The distribution of homogeneous and non homogeneous quadratic functions of normal variables, Ann. Math. Statist., 33, 542-570.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 542-570
    • Ruben, H.1
  • 18
    • 0039884906 scopus 로고
    • The distribution of non-negative quadratic forms in normal variables
    • Sheil, J. and O'Muircheartaigh, I. (1977). The distribution of non-negative quadratic forms in normal variables, Applied Statistics, 26, 92-98.
    • (1977) Applied Statistics , vol.26 , pp. 92-98
    • Sheil, J.1    O'Muircheartaigh, I.2
  • 19
    • 0004537632 scopus 로고
    • Distribution of a sum of weighted chi-square variables
    • Solomon, H. and Stephens, M. A. (1977). Distribution of a sum of weighted chi-square variables, J. Amer. Statist. Assoc., 72, 881-885.
    • (1977) J. Amer. Statist. Assoc. , vol.72 , pp. 881-885
    • Solomon, H.1    Stephens, M.A.2
  • 20
    • 0002878311 scopus 로고
    • Tests based on EDF statistics
    • Chapter 4, Marcel & Decker, New York
    • Stephens, M. A. (1986). Tests based on EDF statistics, Chapter 4, Goodness-of-Fit Techniques, Marcel & Decker, New York.
    • (1986) Goodness-of-fit Techniques
    • Stephens, M.A.1
  • 22
    • 79955400567 scopus 로고
    • Obtaining distribution functions by numerical inversion of characteristic functions with application
    • Waller, L. A., Turnbull, B. W. and Hardin, J. M. (1995). Obtaining distribution functions by numerical inversion of characteristic functions with application, Amer. Statist, 49, 346-350.
    • (1995) Amer. Statist , vol.49 , pp. 346-350
    • Waller, L.A.1    Turnbull, B.W.2    Hardin, J.M.3
  • 23
    • 84972924207 scopus 로고
    • An F approximation to the distribution of a linear combination of chi-squared variables
    • Wood, A. T. A. (1989). An F approximation to the distribution of a linear combination of chi-squared variables, Commun. Statist. Simulation Comput., 18, 1439-1456.
    • (1989) Commun. Statist. Simulation Comput. , vol.18 , pp. 1439-1456
    • Wood, A.T.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.