VGAM (version 1.0-1)

expexpff1: Exponentiated Exponential Distribution

Description

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

Usage

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

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.

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.

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