论文信息 - EXPRESSIONS FOR INVERSE MOMENTS OF POSITIVE QUADRATIC FORMS IN NORMAL VARIABLES

EXPRESSIONS FOR INVERSE MOMENTS OF POSITIVE QUADRATIC FORMS IN NORMAL VARIABLES

Summary A unified approach to the provision of exact expressions for inverse moments of positive quadratic forms in normal variables is described, using the method of (essentially) integrating the moment-generating-function (Cressie, Davis, Folks & Policello (1981). A number of special cases, many familiar from the literature, are reviewed; some allow closed form representations, others are expressed in terms of well-known mathematical functions. In the general case, our approach affords representations suitable for numerical computations.

M. C. Jones

[1] George G. Judge,et al. A simple form for the inverse moments of non-central χ2 andF random variables and certain confluent hypergeometric functions , 1984 .

[2] J. Dickey. Multiple Hypergeometric Functions: Probabilistic Interpretations and Statistical Uses , 1983 .

[3] H. Robbins,et al. Application of the Method of Mixtures to Quadratic Forms in Normal Variates , 1949 .

[4] D. L. Thomas. Reciprocal Moments of Linear Combinations of Exponential Variates , 1976 .

[5] P. Laycock,et al. An explicit formula for the risk of James-Stein estimators , 1982 .

[6] N. Cressie,et al. The Moment-Generating Function and Negative Integer Moments , 1981 .

[7] S. Zacks,et al. A mixture approximation to the distribution of a weighted sum of chi-squared variables , 1981 .

[8] An exact formula for the mean squared error of the inverse estimator in the linear calibration problem , 1985 .

[9] Lauricella's hypergeometric function FD☆ , 1963 .