VGAM (version 1.1-3)

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)
# }