momentchi2 (version 0.1.5)

wf: Wood's F method

Description

Computes the cdf of a positively-weighted sum of chi-squared random variables with the Wood F (WF) method.

Usage

wf(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.

Details

Note that there are pathological cases where, for certain coefficient vectors (which result in certain cumulant values), the Wood F method will be unable to match moments (cumulants) with the three-parameter F distribution. In this situation, the HBE method is used, and a warning is displayed. A simple example of such a pathological case is when the coefficient vector is of length 1. Note that these pathological cases are rare; see (Wood, 1989) in the references.

References

• A. T. A. Wood. An F approximation to the distribution of a linear combination of chi-squared variables. Communications in Statistics-Simulation and Computation, 18(4):1439-1456, 1989.

Examples

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

wf(c(1.5, 1.5, 0.5, 0.5), 10.203)            # should give value close to 0.95
wf(coeff=c(1.5, 1.5, 0.5, 0.5), x=10.203)    # specifying parameters
wf(c(1.5, 1.5, 0.5, 0.5), c(0.627, 10.203))  # x is a vector, output approx. 0.05, 0.95
wf(c(0.9), 1)                                # pathological case, warning, uses hbe()