weibull.mean {VGAM} | R Documentation

## Weibull Distribution Family Function, Parameterized by the Mean

### Description

Maximum likelihood estimation of the 2-parameter Weibull distribution. The mean is one of the parameters. No observations should be censored.

### Usage

    weibull.mean(lmean = "loge", lshape = "loge", imean = NULL,
                 ishape = NULL, probs.y = c(0.2, 0.5, 0.8),
                 imethod = 1, zero = "shape")

### Arguments

`lmean, lshape` | Parameter link functions applied to the (positive) mean parameter (called mu below) and (positive) shape parameter (called a below). See `Links` for more choices.
`imean, ishape` | Optional initial values for the mean and shape parameters.
`imethod, zero, probs.y` | Details at `CommonVGAMffArguments`.

### Details

See `weibullR` for most of the details for this family function too. The mean of Y is b * gamma(1+ 1/a) (returned as the fitted values), and this is the first parameter (a `loge` link is the default because it is positive). The other parameter is the positive shape paramter a, also having a default `loge` link.

This VGAM family function currently does not handle censored data. Fisher scoring is used to estimate the two parameters. Although the expected information matrices used here are valid in all regions of the parameter space, the regularity conditions for maximum likelihood estimation are satisfied only if a>2 (according to Kleiber and Kotz (2003)). If this is violated then a warning message is issued. One can enforce a>2 by choosing `lshape = logoff(offset = -2)`. Common values of the shape parameter lie between 0.5 and 3.5.

### Value

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

### Note

See `weibullR` for more details. This VGAM family function handles multiple responses.

### Author(s)

T. W. Yee

### See Also

`weibullR`, `dweibull`, `truncweibull`, `gev`, `lognormal`, `expexpff`, `maxwell`, `rayleigh`, `gumbelII`.

### Examples

    wdata <- data.frame(x2 = runif(nn <- 1000))  # Complete data
    wdata <- transform(wdata, mu     = exp(-1 + 1 * x2),
                              x3     = rnorm(nn),
                              shape1 = exp(1),
                              shape2 = exp(2))
    wdata <- transform(wdata,
      y1 = rweibull(nn, shape = shape1, scale = mu / gamma(1 + 1/shape1)),
      y2 = rweibull(nn, shape = shape2, scale = mu / gamma(1 + 1/shape2)))
    fit <- vglm(cbind(y1, y2) ~ x2 + x3, weibull.mean, data = wdata, trace = TRUE)
    coef(fit, matrix = TRUE)
    sqrt(diag(vcov(fit)))  # SEs
    summary(fit, presid = FALSE)

[Package VGAM version 1.0-3 Index]