expexp1 {VGAM} | R Documentation

## Exponentiated Exponential Distribution

### Description

Estimates the two parameters of the exponentiated exponential distribution by maximizing a profile (concentrated) likelihood.

### Usage

    expexp1(lscale = "loge", escale=list(), iscale = NULL, ishape = 1)

### Arguments

`lscale` | Parameter link function for the (positive) scale parameter. See `Links` for more choices.
`escale` | List. Extra argument for the link. See `earg` in `Links` for general information.
`iscale` | Initial value for the scale parameter. By default, an initial value is chosen internally using `ishape`.
`ishape` | Initial value for the shape parameter. If convergence fails try setting a different value for this argument.

### Details

See `expexp` for details about the exponentiated exponential distribution. This family function uses a different algorithm for fitting the model. Given scale, the MLE of shape can easily be solved in terms of scale. This family function maximizes a profile (concentrated) likelihood with respect to scale. Newton-Raphson is used, which compares with Fisher scoring with `expexp`.

### Value

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

### Warning

The standard errors produced by a `summary` of the model may be wrong.

### Note

This family function works only for intercept-only models, i.e., `y ~ 1` where `y` is the response.

The estimate of shape is attached to the `misc` slot of the object, which is a list and contains the component `shape`.

As Newton-Raphson is used, the working weights are sometimes negative, and some adjustment is made to these to make them positive.

Like `expexp`, good initial values are needed. Convergence may be slow.

### Author(s)

T. W. Yee

### References

Gupta, R. D. and Kundu, D. (2001) Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal, 43, 117–130.

### See Also

`expexp`.

### Examples

    # Ball bearings data (number of million revolutions before failure)
    bbearings = c(17.88, 28.92, 33.00, 41.52, 42.12, 45.60,
    48.80, 51.84, 51.96, 54.12, 55.56, 67.80, 68.64, 68.64,
    68.88, 84.12, 93.12, 98.64, 105.12, 105.84, 127.92,
    128.04, 173.40)
    fit = vglm(bbearings ~ 1, expexp1(ishape=4), trace=TRUE,
               maxit=50, checkwz=FALSE)
    coef(fit, matrix=TRUE)
    Coef(fit) # Authors get c(0.0314, 5.2589) with log-lik -112.9763
    fit@misc$shape    # Estimate of shape
    logLik(fit)

    # Failure times of the airconditioning system of an airplane
    acplane = c(23, 261, 87, 7, 120, 14, 62, 47,
    225, 71, 246, 21, 42, 20, 5, 12, 120, 11, 3, 14,
    71, 11, 14, 11, 16, 90, 1, 16, 52, 95)
    fit = vglm(acplane ~ 1, expexp1(ishape=0.8), trace=TRUE,
               maxit=50, checkwz=FALSE)
    coef(fit, matrix=TRUE)
    Coef(fit) # Authors get c(0.0145, 0.8130) with log-lik -152.264
    fit@misc$shape    # Estimate of shape
    logLik(fit)

[Package VGAM version 0.7-9 Index]