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Original Articles

A mixture approximation to the distribution of a weighted sum of chi-squared variables

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Pages 215-224 | Received 22 Jul 1980, Published online: 20 Mar 2007

References

  • Grad , A. and Solomon , H. 1955 . Distribution of quadratic forms and some applications . Annals of Mathematical Statistics , 25 : 464 – 477 .
  • Imhof , J.P. 1961 . Computing the distribution of quadratic forms in normal variables . Biometrika , 48 : 417 – 426 .
  • Jensen , D.R. and Solomon , H. 1972 . A Gaussian approximation to the distribution of a definite quadratic form . Journal of the American Statistical Association , 67 : 898 – 902 .
  • Johnson , N.L. and Kotz , S. 1970 . Continuous Unicariate Distribution.-2 , Boston, Mass : Houghton-Miillin .
  • Nuets , M.F. and Zackb , S. 1967 . On mixtures of Z 2 and F-distributions which yield distributions of the same family . Ann. Inst. Statist. Math , 19 : 527 – 536 .
  • Robbins , H.E. and Pitman , E.J.G. 1949 . Applications of the method of mixtures to quadratic forms in normal variates . Annals of Mathematical Statistics , 20 : 552 – 560 .
  • Ruben , H. 1962 . Probability concent of regions under spherical distributions. IV. The distribution of homogeneous and nonhomogeneous quadratic functions of normal variables . Annals of mathematical Statistics , 33 : 542 – 570 .
  • Solomon , H. and Stephens , M.A. 1977 . Distribution of a sum of weighted chi-square variables . Journal of the American Statistical Association , 72 : 881 – 885 .
  • Solomon , H. and Stephens , M.A. 1978 . Approximations to density functions using Pearson curves . Journal of the American Statistical Association , 73 : 153 – 160 .

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