sw {momentchi2}

Satterthwaite-Welch method

Description

Computes the cdf of a positively-weighted sum of chi-squared random variables with the Satterthwaite-Welch (SW) method.

Usage

sw(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

• B. L.Welch. The significance of the difference between two means when the population variances are unequal. Biometrika, 29(3/4):350-362, 1938.

• F. E. Satterthwaite. An approximate distribution of estimates of variance components. Biometrics Bulletin, 2(6):110-114, 1946.

• G. E. P. Box Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effects of inequality of variance in the one-way classification. The Annals of Mathematical Statistics, 25(2):290-302, 1954.

Examples

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

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