The Zero/One-Inflated Beta Distribution
Density, distribution function, and random generation for the zero/one-inflated beta distribution.
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)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 * I[0 <= y] + omega_1 * I[1 <= 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.
dzoabeta gives the density,
pzoabeta gives the distribution function,
qzoabeta gives the quantile, and
rzoabeta generates random deviates.
Xiangjie Xue and T. W. Yee
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.