calculating goodness-of-fit statistics

The trouble is log(0/anything) = log(0) = NaN.
Hmm: log(0) = -Inf.

Taka Matzmoto said
I think 0 multiplied by anything should be zero. Am I wrong ?
Yes!  0 * Inf = NaN, 0 * -Inf = NaN, and 0 * NaN = NaN.

Conventionally 0 log0 = 0, since this is the limit of x log x as x -> 0.
That is also what is appropriate in the G^2 formula since it refers to a 
Poisson(0).
If you want them to evaulate to zero you might try zeroing out the 
values you know will be NaN:
X2 = 2*sum(observed*log(observed/expected));
X2[observed==0] = 0;
A trick from way back by Bill Venables is to use pmax(observed, 1) inside 
the log.
--Brett

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Taka Matzmoto
Sent: Tuesday, January 31, 2006 6:03 PM
To: r-help at stat.math.ethz.ch
Subject: [R] calculating goodness-of-fit statistics

Hi R users

I have a simple data for calculating goodness-of-fit statistics (e.g., 
X2 by Pearson, G2 by Wilks)
You have these labelled backwards!
#################################################
observed<-c(424,174,0,402)
expected<-c(282.7174, 314.2972, 142.3142, 260.6712)
2*sum(observed*log(observed/expected)) # for X2
sum((observed-expected)^2/expected)  # for G2
#################################################

(note. expected ones were calculating by a model I used, not by marginal of observed ones.)

The third element of the observed vector is zero.

For third element, 0 * log(0/142.3142) is NaN. That is why I got NaN for G2.

I think 0 multiplied by anything should be zero. Am I wrong ?

Is there any R functions to correct zero cells for calculating G2? If there is, I like to know some

references justifying the correction.

Thank you in advance

TM

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