hbe {momentchi2}

Hall-Buckley-Eagleson method

Description

Computes the cdf of a positively-weighted sum of chi-squared random variables with the Hall-Buckley-Eagleson (HBE) method.

Usage

hbe(coeff, x)

Arguments

coeff

The coefficient vector. All values must be greater than 0.

x

The vector of quantile values. All values must be greater than 0.

References

• P. Hall. Chi squared approximations to the distribution of a sum of independent random variables. The Annals of Probability, 11(4):1028-1036, 1983.

• M. J. Buckley and G. K. Eagleson. An approximation to the distribution of quadratic forms in normal random variables. Australian Journal of Statistics, 30(1):150-159, 1988.

Examples

#Examples taken from Table 18.6 in N. L. Johnson, S. Kotz, N. Balakrishnan.
#Continuous Univariate Distributions, Volume 1, John Wiley & Sons, 1994.

hbe(c(1.5, 1.5, 0.5, 0.5), 10.203)            # should give value close to 0.95
hbe(coeff=c(1.5, 1.5, 0.5, 0.5), x=10.203)    # specifying parameters
hbe(c(1.5, 1.5, 0.5, 0.5), c(0.627, 10.203))  # x is a vector, output approx. 0.05, 0.95