Exponentiated Exponential Distribution
Estimates the two parameters of the exponentiated exponential distribution by maximizing a profile (concentrated) likelihood.
expexpff1(lrate = "loglink", irate = NULL, ishape = 1)
lrate |
Parameter link function for the (positive) rate parameter.
See |
irate |
Initial value for the rate parameter.
By default, an initial value is chosen internally using |
ishape |
Initial value for the shape parameter. If convergence fails try setting a different value for this argument. |
See expexpff for details about the exponentiated
exponential distribution. This family function uses a different
algorithm for fitting the model. Given rate,
the MLE of shape can easily be solved in terms of
rate. This family function maximizes a profile
(concentrated) likelihood with respect to rate.
Newton-Raphson is used, which compares with Fisher scoring with
expexpff.
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 expexpff, 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)
edata <- data.frame(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, expexpff1(ishape = 4), trace = TRUE,
maxit = 250, checkwz = FALSE, data = edata)
coef(fit, matrix = TRUE)
Coef(fit) # Authors get c(0.0314, 5.2589) with log-lik -112.9763
logLik(fit)
fit@misc$shape # Estimate of shape
# Failure times of the airconditioning system of an airplane
eedata <- data.frame(acplane = c(23, 261, 87, 7, 120, 14, 62, 47,
225, 71, 246, 21, 42, 20, 5, 12, 120, 11, 3, 14,
71, 11, 14, 11, 16, 90, 1, 16, 52, 95))
fit <- vglm(acplane ~ 1, expexpff1(ishape = 0.8), trace = TRUE,
maxit = 50, checkwz = FALSE, data = eedata)
coef(fit, matrix = TRUE)
Coef(fit) # Authors get c(0.0145, 0.8130) with log-lik -152.264
logLik(fit)
fit@misc$shape # Estimate of shapePlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.