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

## Description

Density, distribution function, quantile function and random generation for the univariate beta-normal distribution.

## Usage

 ```1 2 3 4 5 6``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## 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 ## End(Not run) ```

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.