rmutil: BetaBinom – R documentation

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BetaBinom

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

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

Utilities for Nonlinear Regression and Repeated Measurements Models

v1.1.5

GPL-2

Authors

Bruce Swihart [cre, aut], Jim Lindsey [aut] (Jim created this package, Bruce is maintaining the CRAN version)

Initial release