VGAM (version 1.1-9)

lindley: 1-parameter Gamma Distribution

Description

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

Usage

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

Value

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

and vgam.

Arguments

link

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

itheta, zero

See CommonVGAMffArguments for information.

Author

T. W. Yee

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

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)