VGAM (version 1.1-5)

lindley: 1-parameter Gamma Distribution

Description

Estimates the (1-parameter) Lindley distribution by maximum likelihood estimation.

Usage

lindley(link = "loglink", itheta = NULL, zero = NULL)

Arguments

link

Link function applied to the (positive) parameter. See Links for more choices.

itheta, zero

See CommonVGAMffArguments for information.

Value

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

Details

The density function is given by $$f(y; \theta) = \theta^2 (1 + y) \exp(-\theta y) / (1 + \theta)$$ for \(\theta > 0\) and \(y > 0\). The mean of \(Y\) (returned as the fitted values) is \(\mu = (\theta + 2) / (\theta (\theta + 1))\). The variance is \((\theta^2 + 4 \theta + 2) / (\theta (\theta + 1))^2\).

References

Lindley, D. V. (1958). Fiducial distributions and Bayes' theorem. Journal of the Royal Statistical Society, Series B, Methodological, 20, 102--107.

Ghitany, M. E. and Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application. Math. Comput. Simul., 78, 493--506.

See Also

dlind, gammaR, simulate.vlm.

Examples

# NOT RUN {
ldata <- data.frame(y = rlind(n = 1000, theta = exp(3)))
fit <- vglm(y ~ 1, lindley, data = ldata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)
# }