## dbetabinom versions

I got this email from a student:

(1) I used the following R function in package “emdbook

```dbetabinom(x,prob,size,theta, shape1,shape2,log=FALSE)
```

more precisely I did

```curve(dbetabinom(x,size=15,shape1=3,shape2=7),ylim=c(0,.12),xlim=c(0,10))
```

(2) instead I use the following R function in package “VGAM

```dbetabinom.ab(x,size,shape1,shape2,log=FALSE,.dontuse.prob=NULL)
```

more precisely I did

```curve(dbetabinom.ab(x,size=15,shape1=3,shape2=7),ylim=c(0,.12),xlim=c(0,10))
```

and I get two different curves! Sad!

to which I replied only the following

```> dbetabinom.ab(1:10,size=15,shape1=3,shape2=7)
[1] 0.08893281 0.12450593 0.14198045 0.14198045 0.12861758
[6] 0.10718132 0.08268273 0.05905909 0.03886795 0.02332077
> dbetabinom(1:10,size=15,shape1=3,shape2=7)
[1] 0.08893281 0.12450593 0.14198045 0.14198045 0.12861758
[6] 0.10718132 0.08268273 0.05905909 0.03886795 0.02332077
```

as the beta-binomial density is only defined for integers! (emdbook is the R package associated with Benjamin Bolker’s Ecological Models and Data in R.)

### 5 Responses to “dbetabinom versions”

1. A couple of points:

* The reason dbetabinom acts strangely is that I use `lchoose()` (log(C(n,k)) internally, which does the rounding — but `lbeta()`, which is also used, does *not* round … I will fix `dbetabinom()` to behave like `dbinom()`. (Arguably `dbetabinom.ab()` should issue a warning for non-integer x too, for consistency with R’s other distribution functions …)
* I would suggest to the student that if they want to use `curve()`, they try

curve(dbetabinom(x,size=15,shape1=3,shape2=7),
ylim=c(0,.12),xlim=c(0,10),n=11,type=”h”)

• Thanks! I still do not think ‘curve()’ is appropriate in this case…

• did you look at what I actually did there with curve()? I use n=11 to make sure the function only gets evaluated at integer values, and type=”h” to draw vertical indicator lines rather than connecting the densities (which I agree would be inappropriate). Admittedly it might be better to just evaluate the function at the integers “by hand” and use plot(…,type=”h”), but one would end up with the same plot.

• sorry for being cryptic: I meant that finite support pdfs should not be drawn using a continuous curve tool like curve(), and agree that plot() would be better.

2. dbetabinom (package emdbook) does behave strangely. When you call it at a non-integer value, it does not return 0. Instead, you get a warning stating that the value was rounded to the nearest integer.
BUT: calling

```dbetabinom(2,size=15,shape1=3,shape2=7)
```

and

```dbetabinom(1.9,size=15,shape1=3,shape2=7)
```

return different values. In the formula for the density, the value of x is sometimes rounded to the nearest integer, sometimes not. So the output value is completely meaningless.

```dbetabinom.ab (package VGAM)
```

seems to behave more reasonably, returning 0 for non integer values of x.