Re: [SPSSX-L] Negative Binomial – SPSS Bug (?)

Posted by Jon K Peck on Sep 11, 2012; 12:50pm
URL: http://spssx-discussion.165.s1.nabble.com/Negative-Binomial-SPSS-Bug-tp5715014p5715016.html

There are two different parameterizations of the negative binomial in common usage.  You are  probably looking at definitions for a different parameterization than SPSS uses.

Look at http://en.wikipedia.org/wiki/Negative_binomial_distribution and the SPSS function help for details.

Jon Peck (no "h") aka Kim
Senior Software Engineer, IBM
[hidden email]
new phone: [phone]




From:        drfg2008 <[hidden email]>
To:        [hidden email]
Date:        09/11/2012 05:03 AM
Subject:        [SPSSX-L] Negative Binomial – SPSS Bug (?)
Sent by:        "SPSSX(r) Discussion" <[hidden email]>

---

[This thread refers to the thread: "Poisson - negative binomial" Dec. 19,
2011 and Sep 06, 2012]

I have E(X) and V(X) of a neg.bin. distributed RV and would like to compute
the cumulative Neg. Bin. function for P(X<=2).
CDF.NEGBIN(quant,thresh,prob)

---------------------
According to my textbook [1]
E(X)= k(1-p)/p
V(X)=k(1-p)/p^2
p = E(x)/V(x)
k= E(X) p(1-p)
(where p is the probability and k is the threshold)
--------------------

Example:
E(x) = 1.0815
V(x) = 1.7697
->  p = 0.611, k = 1.7
--------------------
My problem is that I do not get the results of the SPSS function reproduced
. In the described example the result should be 0.8694. Instead SPSS
computes 0.5366.
See for example this python  recursive version:

begin program.
import math
import spss

def negbin(x,k,p):
if x==0:
 return math.pow(p,k)
return negbin(x-1,k,p)*(1-p)*(x-1+k)/(x-1+1)

def VertNegBin(x,k,p):
zaehler=x
summe=0
while zaehler>=0:
 summe=summe+negbin(zaehler,k,p)
 zaehler=zaehler-1
return summe
end program.

*----------------------------------------------------------------.
COMPUTE var = 1.7697.
COMPUTE Lambda_f = 1.0815.
compute wert=2.
*----------------------------------------------------------------.

COMPUTE negProb=LAMBDA_F/var.
COMPUTE thresh=LAMBDA_F*(negProb/(1-negProb)).
execute.

spssinc trans result=CDFnegBinResult /Formula "VertNegBin(      wert,
thresh,negProb)".
execute.

spssinc trans result=PDFnegBinResult /Formula "negbin(  wert,
thresh,negProb)".
execute.


COMPUTE SPSS_version=CDF.NEGBIN(wert,thresh,negProb).
EXECUTE.

My question: Is it an SPSS Bug or my misunderstanding of thresh and prob in
the SPSS function, and if the last applies, how then to compute
CDF.NEGBIN(quant,thresh,prob) ?

Literature:
[1] Schlittgen, R.: Einführung in die Statistik. 5. Auflg.  Oldenbourg 1995,
S.203 ff




-----
Dr. Frank Gaeth
FU-Berlin

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