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 0.7-7 Index]