# betanormUC: The Beta-Normal Distribution In VGAM: Vector Generalized Linear and Additive Models

 Betanorm 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 `runif`. `shape1, shape2` the two (positive) shape parameters of the standard beta distribution. They are called `a` and `b` respectively in `beta`. `mean, sd` the mean and standard deviation of the univariate normal distribution (`Normal`). `log, log.p` Logical. If `TRUE` then all probabilities `p` are given as `log(p)`. `lower.tail` Logical. If `TRUE` then the upper tail is returned, i.e., one minus the usual answer.

### 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.

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)
``````

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