coverage: Calculate coverage probability for a binomial proportion...

In hoehleatsu/binomSamSize: Confidence Intervals and Sample Size Determination for a Binomial Proportion under Simple Random Sampling and Pooled Sampling

Calculate coverage probability for a binomial proportion confidence interval scheme

Description

For a given true value of the proportion compute the coverage probability of the confidence interval

Usage

coverage(ci.fun, n, alpha=0.05, p.grid=NULL,interval=c(0,1),
         pmfX=function(k,n,p) dbinom(k,size=n,prob=p), ...)
## S3 method for class 'coverage'
plot(x, y=NULL, ...)

Arguments

ci.fun	binom.confint like function which computes confidence intervals for a binomial proportion.
n	Sample size of the binomial distribution.
alpha	Level of significance, 1-\alpha is the confidence level.
p.grid	Vector of proportions where to evaluate the confidence interval function. If NULL all those values where the minimum coverage probability can occur is taken. If not NULL then the union between p.grid and these values is taken.
interval	Vector of length two specifying lower and upper border of an interval of interest for the proportion. The intersection of the above grid and this interval is taken.
pmfX	A function based on the arguments k, n and p, giving the probability mass function (pmf) f(x;n,p)=P(X=k;n,p) of X. Typically, this will be the pmf of the binomial distribution.
x	An object of class coverage
y	Not used
...	Further arguments to be sent to ci.fun or the plot function

Details

Compute coverage probabilities for each proportion in p.grid. See actual function code for the exact details, which p.grid is actually chosen.

Value

An object of class coverage containing coverage probabilities, coverage coefficient and more.

Author(s)

M. Höhle

References

Agresti, A. and Coull, B.A. (1998), Approximate is Better than "Exact" for Interval Estimation of Binomial Proportions, The American Statistician, 52(2):119-126.

Examples

#Show coverage of Liu & Bailey interval
cov <- coverage( binom.liubailey, n=100, alpha=0.05,
           p.grid=seq(0,1,length=1000), interval=c(0,1), lambda=0, d=0.1)
plot(cov, type="l")

#Now for some more advanced stuff. Investigate coverage of pooled
#sample size estimators
kk <- 10
nn <- 20
ci.funs <- list(poolbinom.wald, poolbinom.logit, poolbinom.lrt)
covs <- lapply( ci.funs, function(f) {
 coverage( f, n=nn, k=kk, alpha=0.05, p.grid=seq(0,1,length=100),
pmfX=function(k,n,p) dbinom(k,size=n, p=1-(1-p)^kk))
})

par(mfrow=c(3,1))
plot(covs[[1]],type="l",main="Wald",ylim=c(0.8,1))
lines(c(0,1),rep(0.95,2),lty=2,col=2)
plot(covs[[2]],type="l",main="Logit")#,ylim=c(0.8,1))
lines(c(0,1),rep(0.95,2),lty=2,col=2)
plot(covs[[3]],type="l",main="LRT",ylim=c(0.8,1))
lines(c(0,1),rep(0.95,2),lty=2,col=2)

poolbinom.wald(x=1,n=nn,k=kk)
poolbinom.logit(x=1,n=nn,k=kk)
poolbinom.lrt(x=1,n=nn,k=kk)

hoehleatsu/binomSamSize documentation built on March 25, 2024, 10:07 p.m.