dchibarsq {emdbook}

Mixed chi-squared distributions

Description

Calculates "mixed" chi-squared distributions (mixtures of chi-square(n) and chi-square(n-1)); useful for Likelihood Ratio Tests when parameters are on the boundary

Usage

dchibarsq(x, df = 1, mix = 0.5, log = FALSE)
pchibarsq(p, df = 1, mix = 0.5, lower.tail=TRUE, log.p = FALSE)
qchibarsq(q, df = 1, mix = 0.5)
rchibarsq(n, df = 1, mix = 0.5)

Arguments

x

numeric vector of positive values

p

numeric vector of positive values

q

numeric vector of quantiles (0-1)

n

integer: number of random deviates to pick

df

degrees of freedom (positive integer)

mix

mixture parameter: fraction of distribution that is chi-square(n-1) distributed

log

return log densities?

log.p

return log probabilities?

lower.tail

return lower tail values?

Value

Vectors of probability densities (dchibarsq), cumulative probabilities (pchibarsq), quantiles (qchibarsq), or random deviates (rchibarsq) from Goldman and Whelan's "chi-bar-squared" distribution. qchibarsq uses simple algebra for df=1 and uniroot for df>1.

Author(s)

Ben Bolker

References

N. Goldman and S. Whelan (2000) "Statistical Tests of Gamma-Distributed Rate Heterogeneity in Models of Sequence Evolution in Phylogenetics", Mol. Biol. Evol. 17:975-978. D. O. Stram and J. W. Lee (1994) "Variance Components Testing in the Longitudinal Fixed Effects Model", Biometrics 50:1171-1177.

Examples

x <- rchibarsq(100)
plot(density(x,from=0))
curve(dchibarsq(x),add=TRUE,col=2,from=0)
## Not run: 
library(lattice)
print(qqmath(~ simdist,
       distribution=qchibarsq,
       panel = function(x, ...) {
         panel.qqmathline(x, ...)
         panel.qqmath(x, ...)
            }))


## End(Not run)
## create first line of table in Goldman and Whelan 2000
round(qchibarsq(c(0.01,0.05,0.9,0.95,0.975,0.99,0.995),df=1),2)
## check second line of table
round(pchibarsq(c(3.81,5.14,6.48,8.27,9.63),df=2),3)
## create middle column
round(qchibarsq(0.95,df=1:10))