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)