Documentation Update for Beta Binomial

[sjenkins20]

The documentation for the beta binomial distribution in the library rmutil appears to be incorrect. The equation makes reference to \mu and \sigma, but there is no reference to them in the inputs.

From a useability point of view, it would also be useful if there was a reference to how the variables relate to the standard notation for the distribution i.e.: the parameters alpha and beta.

[swihart]

I'm looking into doing some edits. I need a couple of days to do so. Would you care to give me a link you use for "standard notation"?

[swihart]

Looks like the parameterizations go like this --

# The beta binomial distribution with total = n and prob = m has density
# 
# p(y) = B(y+s m,n-y+s (1-m)) Choose(n,y) / B(s m,s (1-m))
# 
# for y = 0, …, n where B() is the beta function.

## in `rmutil` from the .Rd file (excerpt above), the "alpha" is s*m
## in `rmutil` from the .Rd file (excerpt above), the "beta"  is s*(1-m)

## in `VGAM`, rho is 1/(1+alpha+beta)

qq = 2.2
zz = 100

alpha = 1.1
beta  = 2
VGAM::pbetabinom.ab(q=qq, size=zz, shape1=alpha, shape2=beta)

## for VGAM `rho`
rr = 1/(1+alpha+beta)
VGAM::pbetabinom   (q=qq, size=zz, prob=mm, rho = rr)

## for rmutil `m` and `s`:
mm = alpha / (alpha+beta)
ss = (alpha+beta)
rmutil::pbetabinom(q=qq, size=zz, m=mm, s=ss )

executed:

> qq = 2.2
> zz = 100
> alpha = 1.1
> beta  = 2
> VGAM::pbetabinom.ab(q=qq, size=zz, shape1=alpha, shape2=beta)
[1] 0.04367989
> ## for VGAM `rho`
> rr = 1/(1+alpha+beta)
> VGAM::pbetabinom   (q=qq, size=zz, prob=mm, rho = rr)
[1] 0.04367989
> ## for rmutil `m` and `s`:
> mm = alpha / (alpha+beta)
> ss = (alpha+beta)
> rmutil::pbetabinom(q=qq, size=zz, m=mm, s=ss )
[1] 0.04367989

This seem right to you? Anchor it in VGAM's (and wikipedia's) parameterization using alpha and beta and then express everything else in term of alpha and beta?

[swihart]

Also added it to the arguments section. Thanks!