poisson.blaker.acc {BlakerCI}  R Documentation 
Blaker's Poisson acceptability function, optionally unimodalized.
Description
Calculates values of the acceptability function for the Poisson distribution (see Blaker (2000)) in a sequence of points (for, e.g., plotting purposes). The acceptability function may optionally be “unimodalized”, i.e. replaced with the smallest greater or equal unimodal function.
Usage
poisson.blaker.acc(x, p, type = c("orig", "unimod"),
acc.tol = 1e10, ...)
Arguments
x 
number of events. 
p 
vector (length 1 allowed) of hypothesized Poisson parameters. In case of more than one point, an increasing sequence required. 
type 
for 
acc.tol 
numerical tolerance (relevant only for 
... 
additional arguments to be passed to

Details
Single values of the “unimodalized” acceptability function
(for type = "unimod"
) are computed by an iterative
numerical algorithm implemented in internal function
poisson.blaker.acc.single.p
.
The function cited is called just once in each of the intervals
where the acceptability function is continuous
(namely in the leftmost one of those points of p
that fall into the interval when dealing with points
below x
, and the rightmost one when above
x
). The rest is done by function
cummax
.
This is considerably faster than calling
poisson.blaker.acc.single.p
for every point of p
.
Note that applying cummax
directly to
a vector of unmodified acceptability values
is even faster and provides a unimodal output;
it may, nevertheless, lack accuracy.
Value
Vector of acceptability values (with or without unimodalization)
in points of p
.
Note
Inspired by M.P. Fay (2010), mentioning “unavoidable inconsistencies” between tests with nonunimodal acceptability functions and confidence intervals derived from them. When the acceptability functions are unimodalized and the test modified accordingly (i.e. pvalues slightly increased in some cases), a perfectly matching testCI pair is obtained.
Author(s)
Jan Klaschka klaschka@cs.cas.cz
References
Blaker, H. (2000) Confidence curves and improved exact confidence
intervals for discrete distributions.
Canadian Journal of Statistics 28: 783798.
(Corrigenda: Canadian Journal of Statistics 29: 681.)
Fay, M.P. (2010). Twosided Exact Tests and Matching Confidence Intervals for Discrete Data. R Journal 2(1): 5358.
Examples
p < seq(0,10,length=1001)
acc < poisson.blaker.acc(3,p)
acc1 < poisson.blaker.acc(3,p,type="unimod")
plot(p,acc,type="l")
lines(p,acc1,col="red")
legend(x=7,y=.8,c("orig","unimod"),col=c("black","red"),lwd=1)
## The two lines  the unimodalized and original acceptabilities 
## look almost the same but some small differences are slightly
## visible.
## They can be seen better this way:
plot(p,acc1acc,type="l")
## Focussing on one of them:
p < seq(5.05,5.6,length=1001)
acc < poisson.blaker.acc(3,p)
acc1 < poisson.blaker.acc(3,p,type="unimod")
plot(p,acc,type="l",ylim=c(.391,.396))
lines(p,acc1,col="red")
legend(x=5.4,y=.395,c("orig","unimod"),col=c("black","red"),lwd=1)