expexp1: Exponentiated Exponential Distribution

Description

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

Usage

expexp1(lscale = "loge", escale = list(), iscale = NULL, ishape = 1)

Arguments

lscale

Parameter link function for the (positive) $\lambda$ 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 $\lambda$ 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 expexp 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 expexp.

References

Gupta, R. D. and Kundu, D. (2001) Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal, 43, 117--130.

Examples

Run this code

# Ball bearings data (number of million revolutions before failure)
bbearings = data.frame(y = 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(y ~ 1, expexp1(ishape = 4), bbearings, 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 = data.frame(y = 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(y ~ 1, expexp1(ishape = 0.8), acplane, 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)

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