updog (version 1.1.3)

dbetabinom: The Beta-Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the beta-binomial distribution when parameterized by the mean mu and the overdispersion parameter rho rather than the typical shape parameters.

Usage

dbetabinom(x, size, mu, rho, log)
pbetabinom(q, size, mu, rho, log_p)
qbetabinom(p, size, mu, rho)
rbetabinom(n, size, mu, rho)

Arguments

x, q

A vector of quantiles.

size

A vector of sizes.

mu

Either a scalar of the mean for each observation, or a vector of means of each observation, and thus the same length as x and size. This must be between 0 and 1.

rho

Either a scalar of the overdispersion parameter for each observation, or a vector of overdispersion parameters of each observation, and thus the same length as x and size. This must be between 0 and 1.

log, log_p

A logical vector either of length 1 or the same length as x and size. This determines whether to return the log probabilities for all observations (in the case that its length is 1) or for each observation (in the case that its length is that of x and size).

p

A vector of probabilities.

n

The number of observations.

Value

Either a random sample (rbetabinom), the density (dbetabinom), the tail probability (pbetabinom), or the quantile (qbetabinom) of the beta-binomial distribution.

Functions

• dbetabinom: Density function.

• pbetabinom: Distribution function.

• qbetabinom: Quantile function.

• rbetabinom: Random generation.

Details

Let \(\mu\) and \(\rho\) be the mean and overdispersion parameters. Let \(\alpha\) and \(\beta\) be the usual shape parameters of a beta distribution. Then we have the relation $$\mu = \alpha/(\alpha + \beta),$$ and $$\rho = 1/(1 + \alpha + \beta).$$ This necessarily means that $$\alpha = \mu (1 - \rho)/\rho,$$ and $$\beta = (1 - \mu) (1 - \rho)/\rho.$$

Examples

# NOT RUN {
x <- rbetabinom(n = 10, size = 10, mu = 0.1, rho = 0.01)
dbetabinom(x = 1, size = 10, mu = 0.1, rho = 0.01, log = FALSE)
pbetabinom(q = 1, size = 10, mu = 0.1, rho = 0.01, log_p = FALSE)
qbetabinom(p = 0.6, size = 10, mu = 0.1, rho = 0.01)


# }