maxstat (version 0.7-24)

pLausen92: Approximating Maximally Selected Statistics

Description

Approximates the probability that a maximally selected rank statistic is greater or equal to b.

Usage

pLausen92(b, minprop=0.1, maxprop=0.9)
qLausen92(p, minprop=0.1, maxprop=0.9)

Arguments

b

quantile.

p

probability.

minprop

at least minprop*100% of the observations in the first group.

maxprop

not more than minprop*100% of the observations in the first group.

Value

The probability that, under the hypothesis of independence, a maximally selected statistic greater equal b is observed.

Details

Large sample approximation by Miller and Siegmund (1982) based on a Brownian bridge, cf. Lausen and Schumacher (1992).

References

Miller, R. and Siegmund, D. (1982), Maximally Selected Chi Square Statistics. Biometrics, 38, 1011--1016

Lausen, B. and Schumacher, M. (1992), Maximally Selected Rank Statistics. Biometrics, 48, 73--85

Examples

# Compute quantiles. Should be equal to Table 2 in Lausen and Schumacher

load(file.path(system.file(package = "maxstat"), "results", "LausenTab2.rda"))

a <- rev(c(0.01, 0.025, 0.05, 0.1))
prop <- rbind(c(0.25, 0.75), c(0.4, 0.6), c(0.1, 0.9), c(0.4, 0.9))
Quant <- matrix(rep(0, length(a)*nrow(prop)), nrow=length(a)) 

for (i in 1:length(a)) {                                            
  for (j in 1:nrow(prop)) {                            
    Quant[i,j] <- qLausen92(a[i], minprop=prop[j,1], maxprop=prop[j,2]) 
  }
}

Quant <- round(Quant, 3)
rownames(Quant) <- a
colnames(Quant) <- c("A2575", "A46", "A19", "A49")
Quant <- as.data.frame(Quant)
rownames(LausenTab2) <- a

Quant

LausenTab2

if(!all.equal(LausenTab2, Quant)) stop("error checking pLausen92")