# zoabetaUC: The Zero/One-Inflated Beta Distribution In VGAM: Vector Generalized Linear and Additive Models

 Zoabeta R Documentation

## The Zero/One-Inflated Beta Distribution

### Description

Density, distribution function, and random generation for the zero/one-inflated beta distribution.

### Usage

dzoabeta(x, shape1, shape2, pobs0 = 0, pobs1 = 0, log = FALSE,
tol = .Machine$double.eps) pzoabeta(q, shape1, shape2, pobs0 = 0, pobs1 = 0, lower.tail = TRUE, log.p = FALSE, tol = .Machine$double.eps)
qzoabeta(p, shape1, shape2, pobs0 = 0, pobs1 = 0,
lower.tail = TRUE, log.p = FALSE, tol = .Machine$double.eps) rzoabeta(n, shape1, shape2, pobs0 = 0, pobs1 = 0, tol = .Machine$double.eps)


### Arguments

 x, q, p, n Same as Beta. pobs0, pobs1 vector of probabilities that 0 and 1 are observed (\omega_0 and \omega_1). shape1, shape2 Same as Beta. They are called a and b in beta respectively. lower.tail, log, log.p Same as Beta. tol Numeric, tolerance for testing equality with 0 and 1.

### Details

This distribution is a mixture of a discrete distribution with a continuous distribution. The cumulative distribution function of Y is

F(y) =(1 - \omega_0 -\omega_1) B(y) + \omega_0 \times I[0 \leq y] + \omega_1 \times I[1 \leq y]

where B(y) is the cumulative distribution function of the beta distribution with the same shape parameters (pbeta), \omega_0 is the inflated probability at 0 and \omega_1 is the inflated probability at 1. The default values of \omega_j mean that these functions behave like the ordinary Beta when only the essential arguments are inputted.

### Value

dzoabeta gives the density, pzoabeta gives the distribution function, qzoabeta gives the quantile, and rzoabeta generates random deviates.

### Author(s)

Xiangjie Xue and T. W. Yee

zoabetaR, beta, betaR, Betabinom.

### Examples

## Not run:
N <- 1000; y <- rzoabeta(N, 2, 3, 0.2, 0.2)
hist(y, probability = TRUE, border = "blue", las = 1,
main = "Blue = 0- and 1-altered; orange = ordinary beta")
sum(y == 0) / N  # Proportion of 0s
sum(y == 1) / N  # Proportion of 1s
Ngrid <- 1000
lines(seq(0, 1, length = Ngrid),
dbeta(seq(0, 1, length = Ngrid), 2, 3), col = "orange")
lines(seq(0, 1, length = Ngrid), col = "blue",
dzoabeta(seq(0, 1, length = Ngrid), 2 , 3, 0.2, 0.2))

## End(Not run)


VGAM documentation built on Sept. 19, 2023, 9:06 a.m.