survey (version 3.9-1)

pchisqsum: Distribution of quadratic forms

Description

The distribution of a quadratic form in p standard Normal variables is a linear combination of p chi-squared distributions with 1df. This function provides the cumulative distribution function by numerical inversion of the characteristic function and also provides the Satterthwaite approximation.

Usage

pchisqsum(x, df, a, lower.tail = TRUE, method = c("satterthwaite", "integration"))

Arguments

x
Observed values
df
Vector of degrees of freedom
a
Vector of coefficients
lower.tail
lower or upper tail?
method
Satterthwaite approximation or numerical integration?

Value

  • Vector of cumulative probabilities

See Also

pchisq

Examples

Run this code
x <- 5*rnorm(1001)^2+rnorm(1001)^2
x.thin<-sort(x[1+(0:50)*20])
p.invert<-pchisqsum(x.thin,df=c(1,1),a=c(5,1),method="integration")
p.satt<-pchisqsum(x.thin,df=c(1,1),a=c(5,1),method="satt")

plot(p.invert, p.satt,type="l")
abline(0,1,lty=2,col="purple")

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