# BetaBinom: Beta Binomial Distribution In rmutil: Utilities for Nonlinear Regression and Repeated Measurements Models

 Beta Binomial R Documentation

## Beta Binomial Distribution

### Description

These functions provide information about the beta binomial distribution with parameters `m` and `s`: density, cumulative distribution, quantiles, and random generation. Compared to the parameterization of 'VGAM::pbetabinom.ab', `m = alpha/(alpha+beta)` and `s = (alpha+beta)`. See examples.

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.

### Usage

```dbetabinom(y, size, m, s, log=FALSE)
pbetabinom(q, size, m, s)
qbetabinom(p, size, m, s)
rbetabinom(n, size, m, s)
```

### Arguments

 `y` vector of frequencies `q` vector of quantiles `p` vector of probabilities `n` number of values to generate `size` vector of totals `m` vector of probabilities of success; Compared to the parameterization of 'VGAM::pbetabinom.ab', `m = alpha/(alpha+beta)` where `shape1=alpha` and `shape2=beta`. See examples. `s` vector of overdispersion parameters; Compared to the parameterization of 'VGAM::pbetabinom.ab', `s = (alpha+beta)` where `shape1=alpha` and `shape2=beta`. See examples. `log` if TRUE, log probabilities are supplied.

### Author(s)

J.K. Lindsey

`dbinom` for the binomial, `ddoublebinom` for the double binomial, and `dmultbinom` for the multiplicative binomial distribution.

### Examples

```# compute P(45 < y < 55) for y beta binomial(100,0.5,1.1)
sum(dbetabinom(46:54, 100, 0.5, 1.1))
pbetabinom(54,100,0.5,1.1)-pbetabinom(45,100,0.5,1.1)
pbetabinom(2,10,0.5,1.1)
qbetabinom(0.33,10,0.5,1.1)
rbetabinom(10,10,0.5,1.1)
## compare to VGAM
## Not run:
# 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 )

## End(Not run)
```

rmutil documentation built on March 18, 2022, 6:55 p.m.