[R] poisson mean hypothesis
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Mon Sep 12 16:50:42 CEST 2005
Thomas Lumley <tlumley at u.washington.edu> writes:
> Use ppois(x,lambda), which gives P(X<=x) for mean=lambda.
>
> Eg: lower one-sided test for observing no events with mean of 3.4
> > ppois(0,3.4)
> [1] 0.03337327
>
> upper one-sided test for observing 8 events with a mean of 3.4 (need the
> -1 to include 8 in the rejection region)
>
> > ppois(8-1,3.4,lower.tail=FALSE)
> [1] 0.02307394
>
> If you want an exact confidence interval there is a formula involving the
> quantiles of the gamma distribution (ie the qgamma() function) that I
> can't remember off hand. It might even be Garwood's formula.
Or you can clone the procedure in binom.test. In fact, using
binom.test with a sufficiently large n is a rather decent "cheat":
> binom.test(5,1e6)$conf * 1e6
[1] 1.623488 11.668293
attr(,"conf.level")
[1] 0.95
> ppois(4,1.623488)
[1] 0.975
> ppois(5,11.668293)
[1] 0.02500060
The qgamma-based interval would seem to be from
> qgamma(.025, 5)
[1] 1.623486
to
> qgamma(1 - .025, 5 + 1)
[1] 11.66833
Notice that this is obtained as the intersection of the two one-sided
intervals, each at half the nominal alpha level. There are other
possible definitions (e.g. invert the two sided test), but this one
has the advantage of being computable.
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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