Betanorm {VGAM} | R Documentation |
The Beta-Normal Distribution
Description
Density, distribution function, quantile function and random generation for the univariate beta-normal distribution.
Usage
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)
Arguments
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 |
Details
The function betauninormal
, the VGAM family function
for estimating the parameters,
has not yet been written.
Value
dbetanorm
gives the density,
pbetanorm
gives the distribution function,
qbetanorm
gives the quantile function, and
rbetanorm
generates random deviates.
Author(s)
T. W. Yee
References
Gupta, A. K. and Nadarajah, S. (2004). Handbook of Beta Distribution and Its Applications, pp.146–152. New York: Marcel Dekker.
Examples
## 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 = paste0("betanorm(",shape1,", ",shape2,", m=",m, ", sd=1)"),
main = "Blue is density, orange is the CDF",
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
## End(Not run)