| expexp1 {VGAM} | R Documentation |
Estimates the two parameters of the exponentiated exponential distribution by maximizing a profile (concentrated) likelihood.
expexp1(lscale = "loge", escale=list(), iscale = NULL, ishape = 1)
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.
|
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.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm
and vgam.
The standard errors produced by a
summary of the model may be wrong.
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.
T. W. Yee
Gupta, R. D. and Kundu, D. (2001) Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal, 43, 117–130.
# 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)