gamma1 {VGAM} | R Documentation

## 1-parameter Gamma Distribution

### Description

Estimates the 1-parameter gamma distribution by maximum likelihood estimation.

### Usage

    gamma1(link = "loge", earg=list())

### Arguments

`link` | Link function applied to the (positive) shape parameter. See `Links` for more choices.
`earg` | List. Extra argument for the link. See `earg` in `Links` for general information.

### Details

The density function is given by

f(y) = exp(-y) y^(shape-1) / gamma(shape)

for shape > 0 and y > 0. Here, gamma(shape) is the gamma function, as in `gamma`. The mean of Y (returned as the fitted values) is mu=shape, and the variance is sigma^2 = shape.

### 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 a multivariate (matrix) response.

The parameter shape matches with `shape` in `rgamma`. The argument `rate` in `rgamma` is assumed 1 for this family function.

If rate is unknown use the family function `gamma2.ab` to estimate it too.

### Author(s)

T. W. Yee

### References

Most standard texts on statistical distributions describe the 1-parameter gamma distribution, e.g.,

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

### See Also

`gamma2.ab` for the 2-parameter gamma distribution, `lgammaff`.

### Examples

    y = rgamma(n=100, shape= exp(3))
    fit = vglm(y ~ 1, gamma1, trace=TRUE, crit="c")
    coef(fit, matrix=TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 0.7-9 Index]