betaR {VGAM} | R Documentation

## The Two-parameter Beta Distribution Family Function

### Description

Estimation of the shape parameters of the two-parameter beta distribution.

### Usage

    betaR(lshape1 = "loglink", lshape2 = "loglink",
          i1 = NULL, i2 = NULL, trim = 0.05,
          A = 0, B = 1, parallel = FALSE, zero = NULL)

### Arguments

`lshape1, lshape2, i1, i2` | Details at `CommonVGAMffArguments`. See `Links` for more choices.
`trim` | An argument which is fed into `mean()`; it is the fraction (0 to 0.5) of observations to be trimmed from each end of the response `y` before the mean is computed. This is used when computing initial values, and guards against outliers.
`A, B` | Lower and upper limits of the distribution. The defaults correspond to the standard beta distribution where the response lies between 0 and 1.
`parallel, zero` | See `CommonVGAMffArguments` for more information.

### Details

The two-parameter beta distribution is given by f(y) =

(y-A)^(shape1-1) * (B-y)^(shape2-1) / [Beta(shape1,shape2) * (B-A)^(shape1+shape2-1)]

for A < y < B, and Beta(.,.) is the beta function (see `beta`). The shape parameters are positive, and here, the limits A and B are known. The mean of Y is E(Y) = A + (B-A) * shape1 / (shape1 + shape2), and these are the fitted values of the object.

For the standard beta distribution the variance of Y is shape1 * shape2 / ((1+shape1+shape2) * (shape1+shape2)^2). If σ^2= 1 / (1+shape1+shape2) then the variance of Y can be written mu*(1-mu)*sigma^2 where mu=shape1 / (shape1 + shape2) is the mean of Y.

Another parameterization of the beta distribution involving the mean and a precision parameter is implemented in `betaff`.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, `rrvglm` and `vgam`.

### Note

The response must have values in the interval (A, B). VGAM 0.7-4 and prior called this function `betaff`.

### Author(s)

Thomas W. Yee

### References

Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1995) Chapter 25 of: Continuous Univariate Distributions, 2nd edition, Volume 2, New York: Wiley.

Gupta, A. K. and Nadarajah, S. (2004) Handbook of Beta Distribution and Its Applications, New York: Marcel Dekker.

### See Also

`betaff`, `Beta`, `genbetaII`, `betaII`, `betabinomialff`, `betageometric`, `betaprime`, `rbetageom`, `rbetanorm`, `kumar`, `simulate.vlm`.

### Examples

    bdata <- data.frame(y = rbeta(n = 1000, shape1 = exp(0), shape2 = exp(1)))
    fit <- vglm(y ~ 1, betaR(lshape1 = "identitylink", lshape2 = "identitylink"),
                data = bdata, trace = TRUE, crit = "coef")
    fit <- vglm(y ~ 1, betaR, data = bdata, trace = TRUE, crit = "coef")
    coef(fit, matrix = TRUE)
    Coef(fit)  # Useful for intercept-only models

    bdata <- transform(bdata, Y = 5 + 8 * y)  # From 5 to 13, not 0 to 1
    fit <- vglm(Y ~ 1, betaR(A = 5, B = 13), data = bdata, trace = TRUE)
    Coef(fit)
    c(meanY = with(bdata, mean(Y)), head(fitted(fit),2))

[Package VGAM version 1.1-1 Index]