# [R] Declaring a density function with for loop

chamilka cmanoj4 at gmail.com
Sat Jul 7 12:11:03 CEST 2012

```I have an extended binomial distribution which has the following form:

http://r.789695.n4.nabble.com/file/n4635699/kb.png

Here alpha and beta are two parameters and x=0,1,2,3,...n (alike the
binomial distribution)
I am writing a function to find out the densities (probabilities) of this
distribution for given values of alpha and beta. The below is the my
function...

*dnewdis<-function(x,a,b,n) {
term<-0
for (j in 0:exp(10)) {
term=term+(((-1)**i)*(choose(b-1,i))*(beta(x+a+a*i,n-x+1)))
}
s=a*b*choose(n,x)*term
return(s)
}*

Since the sum inside the pdf runs from 0 to infinity, i restrict it to
exp(10)[a large number)....
My questions are:
1. Does the above function correct for the given pdf?

In a journal paper, this distribution is evaluated for x=0,1,2...7 and n=7
and alpha=0.7 and beta=0.59
so I used my function and got densities as:
/> dnewdis(0,0.7,0.59,7)
[1] 0.9527325
> dnewdis(1,0.7,0.59,7)
[1] 4.001476
> dnewdis(2,0.7,0.59,7)
[1] 10.40384
> dnewdis(3,0.7,0.59,7)
[1] 21.50127
> dnewdis(4,0.7,0.59,7)
[1] 38.70228
> dnewdis(5,0.7,0.59,7)
[1] 63.47174
> dnewdis(6,0.7,0.59,7)
[1] 97.32334
> dnewdis(7,0.7,0.59,7)
[1] 141.814/

which are very contradiction to the values provided in the paper!!!
0.136090
0.104612
0.097393
0.096992
0.101203
0.111303
0.134110
0.218296

Also I am getting probabilities greater than 1 too??

Can you please tell me where am I doing wrong and I the function should be
corrected?

I am a new R user!!

Thank you very much for your kind help!

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