# pLausen92: Approximating Maximally Selected Statistics In maxstat: Maximally Selected Rank Statistics

## Description

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

## Usage

 ```1 2``` ```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.

## Details

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

## Value

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

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```# 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") ```

maxstat documentation built on May 2, 2019, 2:44 a.m.