smoothqpois {cir}R Documentation

Linearly Smoothed Quantile Functions

Description

Provide linearly-interpolated and somewhat modified quantile functions for the binomial and Poisson (as an approximation to the binomial) distributions, for use in interval estimation via 'cir.upndown'. All functions are used to approximate the binomial.

Usage

smoothqpois(p, size, prob, add = FALSE)
smoothqbinom(p, size, prob, add = TRUE,half=FALSE)

Arguments

p The inteval-cutoff quantile points (between 0 and 1). Could be a vector.
size Sample size (for the original binomial problem)
prob True probabilty (center of the interval)
add Whether to add a 'padding' to the output in order to account for randomness in sample size (defaults to FALSE, since it is already accounted for in using Poisson)
half (only for 'smoothqbinom') Should the final outcome shifted by half a unit, for symmetry? Defaults to FALSE

Details

These functions are utilities for 'cir.upndown'. They are tailored to help provide realistic interval estimation for percentile-finding binary experiments in which the treatment allocation is *random*. They make little sense outside this context. See example for how the functions look. For theoretical details, see Oron (2007), Section 3.3.

Value

A vector of the same length as p

Author(s)

Assaf P. Oron

References

Oron A.P., Up-and-Down and the Percentile-Finding Problem. Doctoral Dissertation, University of Washington. 2007

See Also

cir.pava, cir.upndown

Examples


pvec=seq(0,1,.01)

n=10
##### This is for a median-targeting application
targ=0.5

### Plain vanilla binomial (does not account for random allocation, and
### is asymmetric in location of vertical jumps)

plot(100*pvec,qbinom(pvec,size=n,prob=targ),xlab="Cutoff point for
Confidence Interval (percent)",ylab="Confidence Quantile Estimate",type='l')

### Binomial, but linearly interpolated and 'padded'
lines(100*pvec,smoothqbinom(pvec,size=n,prob=targ),col=4)

### Poisson (the preferred approach since it has heavy tails)
lines(100*pvec,smoothqpois(pvec,size=n,prob=targ),col=2)

########## Now the whole thing when the target is 20th percentile

targ=0.2
plot(100*pvec,qbinom(pvec,size=n,prob=targ),xlab="Cutoff point for
Confidence Interval (percent)",ylab="Confidence Quantile Estimate",type='l',ylim=c(-2,10))

lines(100*pvec,smoothqbinom(pvec,size=n,prob=targ),col=4)
lines(100*pvec,smoothqpois(pvec,size=n,prob=targ),col=2)

### A negative value here may seem counter-intuitive, but it makes sense
###in a random-allocation setting
  

[Package cir version 1.0 Index]