R: The Beta-Normal Distribution

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 `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.

### Author(s)

T. W. Yee

### References

pp.146–152 of Gupta, A. K. and Nadarajah, S. (2004) Handbook of Beta Distribution and Its Applications, 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 = 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)

[Package VGAM version 1.0-3 Index]