VGAM (version 1.1-8)

expexpff1: Exponentiated Exponential Distribution

Description

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

Usage

expexpff1(lrate = "loglink", irate = NULL, ishape = 1)

Value

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

and vgam.

Arguments

lrate

Parameter link function for the (positive) \(\lambda\) parameter. See Links for more choices.

irate

Initial value for the \(\lambda\) parameter. By default, an initial value is chosen internally using ishape.

ishape

Initial value for the \(\alpha\) parameter. If convergence fails try setting a different value for this argument.

Author

T. W. Yee

Warning

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

Details

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

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

expexpff, CommonVGAMffArguments.

Examples

# 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 shape