dnbinom(,size<1,)=0 (PR#842)

This came up on r-help but indicates a bug.

dnbinom(x,n,p) calls dbinom_raw(n-1,...)
which returns 0 for n<1.

	-thomas


---------- Forwarded message ----------
Date: Thu, 08 Feb 2001 17:10:23 +0000
From: Yudi Pawitan <yudi@stat.ucc.ie>
To: Mark Myatt <mark@myatt.demon.co.uk>
Cc: R-Help <r-help@stat.math.ethz.ch>
Subject: Re: [R] Goodness of fit to Poisson / NegBinomial

Sorry, Mark, the program worked for Rw1011, but this is
what happened in Rw1021:

dnbinom(0:5,.9,.4)  

[1] 0.4383833 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000   #wrong!!

while, the correct result from Rw1011 is:

 dnbinom(0:5,.9,.4)

[1] 0.43838329 0.23672698 0.13493438 0.07826194 0.04578323 0.02692054

I have added a corrected dnbinom() below, which makes the program
works  for Rw1021.

-YP-

x_ c(70, 38, 17, 10,  9, 6) 
kk_ 0:5
n_ sum(x)

dnbinom_ function(x,n,p){
         gamma(x+n)/gamma(n)/gamma(x+1)*p^n * (1-p)^x
}

fn_ function(p){
    r_ p[1]
    th_ p[2]
    ll _ -sum(x[1:max(kk)]*log(dnbinom(kk[-length(kk)],r,th))) -
          x[length(kk)]*log(1-pnbinom((max(kk)-1),r,th))
    return(ll)
}

a_ nlm(fn,p=c(.9,.5),hes=T)
est_ a$est

phat_ c(dnbinom(kk[-length(kk)],est[1],est[2]),
        1-pnbinom((max(kk)-1),est[1],est[2]))
E_ n*phat
chi2_ sum((x-E)^2/E)
cat('Chi2 goodness-of-fit = ',chi2,'\n')
cat('P-value=',1-pchisq(chi2,df=length(kk)-1-2),'\n')

print(cbind(O=x,E=round(E,1),err=round((x-E)^2/E,1)))


===========================================

Yudi,

Thanks for this:

x_ c(70, 38, 17, 10,  9, 6) 
kk_ 0:5
n_ sum(x)

fn_ function(p){
   r_ p[1]
   th_ p[2]
   ll _ -sum(x[1:max(kk)]*log(dnbinom(kk[-length(kk)],r,th))) -
         x[length(kk)]*log(1-pnbinom((max(kk)-1),r,th))
   return(ll)
}

a_ nlm(fn,p=c(.9,.5),hes=T)
est_ a$est

phat_ c(dnbinom(kk[-length(kk)],est[1],est[2]),
       1-pnbinom((max(kk)-1),est[1],est[2]))
E_ n*phat
chi2_ sum((x-E)^2/E)
cat('Chi2 goodness-of-fit = ',chi2,'\n')
cat('P-value=',1-pchisq(chi2,df=length(kk)-1-2),'\n')

print(cbind(O=x,E=round(E,1),err=round((x-E)^2/E,1)))

It is certainly more elegant than anything I would have come up with but
I just cannot get it to work (Rwin 1.21). The call to nlm() returns:

       Warning messages: 
       1: NA/Inf replaced by maximum positive value 
       2: NA/Inf replaced by maximum positive value 
       3: NA/Inf replaced by maximum positive value 
       4: NA/Inf replaced by maximum positive value 
       5: NA/Inf replaced by maximum positive value 
       6: NA/Inf replaced by maximum positive value 
       7: NA/Inf replaced by maximum positive value 
       8: NA/Inf replaced by maximum positive value 

est holds the starting parameters:

       [1] 0.9 0.5

E (from n*phat) holds:

       [1] 80.38301  0.00000  0.00000  0.00000  0.00000  3.90972

which gives a very big chi-square.

Sorry to be a nuisance.

Mark


--
Mark Myatt

Yudi Pawitan     yudi@stat.ucc.ie
Department of Statistics UCC
Cork, Ireland
Ph   353-21-490 2906
Fax 353-21-427 1040 
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