| pchisqsum {survey} | R Documentation |
The distribution of a quadratic form in p standard Normal variables is a linear combination of p chi-squared distributions with 1df.
pchisqsum(x, df, a, lower.tail = TRUE, method = c("satterthwaite", "integration","saddlepoint"))
x |
Observed values |
df |
Vector of degrees of freedom |
a |
Vector of coefficients |
lower.tail |
lower or upper tail? |
method |
See Details below |
The "satterthwaite" method uses Satterthwaite's approximation,
and this is also used as a fallback for the other methods.
"integration" inverts the characteristic function
numerically. This is relatively slow, and not reliable for p-values
below about 1e-5 in the upper tail, but is highly accurate for moderate p-values.
"saddlepoint" uses a saddlepoint approximation when
x>1.05*sum(a) and the Satterthwaite approximation for
smaller x. This is fast and is accurate in the upper tail, where
accuracy is important.
Vector of cumulative probabilities
Davies RB (1973). "Numerical inversion of a characteristic function" Biometrika 60:415-7
Kuonen D (1999) Saddlepoint Approximations for Distributions of Quadratic Forms in Normal Variables. Biometrika, Vol. 86, No. 4 (Dec., 1999), pp. 929-935
x <- 5*rnorm(1001)^2+rnorm(1001)^2 x.thin<-sort(x)[1+(0:100)*10] p.invert<-pchisqsum(x.thin,df=c(1,1),a=c(5,1),method="int" ,lower=FALSE) p.satt<-pchisqsum(x.thin,df=c(1,1),a=c(5,1),method="satt",lower=FALSE) p.sadd<-pchisqsum(x.thin,df=c(1,1),a=c(5,1),method="sad",lower=FALSE) plot(p.invert, p.satt,type="l",log="xy") abline(0,1,lty=2,col="purple") plot(p.invert, p.sadd,type="l",log="xy") abline(0,1,lty=2,col="purple")