# lindley: 1-parameter Gamma Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 `1` ```lindley(link = "loge", itheta = NULL, zero = NULL) ```

## Arguments

 `link` Link function applied to the (positive) parameter. See `Links` for more choices.
 `itheta, zero` See `CommonVGAMffArguments` for information.

## 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.

## Value

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

## Note

This VGAM family function can handle multiple responses (inputted as a matrix). Fisher scoring is implemented.

T. W. Yee

## 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.

`dlind`, `gammaR`, `simulate.vlm`.
 ```1 2 3 4 5``` ```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) ```