The Beta-Normal Distribution
Density, distribution function, quantile function and random generation for the univariate beta-normal distribution.
dbetanorm(x, shape1, shape2, mean = 0, sd = 1, log = FALSE)
pbetanorm(q, shape1, shape2, mean = 0, sd = 1,
lower.tail = TRUE, log.p = FALSE)
qbetanorm(p, shape1, shape2, mean = 0, sd = 1,
lower.tail = TRUE, log.p = FALSE)
rbetanorm(n, shape1, shape2, mean = 0, sd = 1)x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Same as |
shape1, shape2 |
the two (positive) shape parameters of the standard beta distribution.
They are called |
mean, sd |
the mean and standard deviation of the univariate
normal distribution
( |
log, log.p |
Logical.
If |
lower.tail |
Logical. If |
The function betauninormal, the VGAM family function
for estimating the parameters,
has not yet been written.
dbetanorm gives the density,
pbetanorm gives the distribution function,
qbetanorm gives the quantile function, and
rbetanorm generates random deviates.
T. W. Yee
Gupta, A. K. and Nadarajah, S. (2004). Handbook of Beta Distribution and Its Applications, pp.146–152. New York: Marcel Dekker.
## Not run:
shape1 <- 0.1; shape2 <- 4; m <- 1
x <- seq(-10, 2, len = 501)
plot(x, dbetanorm(x, shape1, shape2, m = m), type = "l", ylim = 0:1, las = 1,
ylab = paste("betanorm(",shape1,", ",shape2,", m=",m, ", sd=1)", sep = ""),
main = "Blue is density, orange is cumulative distribution function",
sub = "Gray lines are the 10,20,...,90 percentiles", col = "blue")
lines(x, pbetanorm(x, shape1, shape2, m = m), col = "orange")
abline(h = 0, col = "black")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qbetanorm(probs, shape1, shape2, m = m)
lines(Q, dbetanorm(Q, shape1, shape2, m = m), col = "gray50", lty = 2, type = "h")
lines(Q, pbetanorm(Q, shape1, shape2, m = m), col = "gray50", lty = 2, type = "h")
abline(h = probs, col = "gray50", lty = 2)
pbetanorm(Q, shape1, shape2, m = m) - probs # Should be all 0
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