geometric {VGAM} | R Documentation

## Geometric Distribution

### Description

Maximum likelihood estimation for the geometric distribution.

### Usage

    geometric(link = "logit", earg=list(), expected = TRUE)

### Arguments

`link` | Parameter link function applied to the parameter prob, which lies in the unit interval. See `Links` for more choices.
`earg` | List. Extra argument for the link. See `earg` in `Links` for general information.
`expected` | Logical. Fisher scoring is used if `expected = TRUE`, else Newton-Raphson.

### Details

A random variable Y has a 1-parameter geometric distribution if P(Y=y) = prob * (1-prob)^y for y=0,1,2,.... Here, prob is the probability of success, and Y is the number of (independent) trials that are fails until a success occurs. Thus the response Y should be a non-negative integer. The mean of Y is E(Y) = (1-prob)/prob and its variance is Var(Y) = (1-prob)/prob^2. The geometric distribution is a special case of the negative binomial distribution (see `negbinomial`).

### Value

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

### Author(s)

T. W. Yee

### References

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

### See Also

`negbinomial`, `Geometric`, `betageometric`, `rbetageom`.

### Examples

    x1 = runif(n <- 1000) - 0.5
    x2 = runif(n) - 0.5
    x3 = runif(n) - 0.5
    eta = 0.2 - 0.7 * x1 + 1.9 * x2
    prob = logit(eta, inverse=TRUE)
    y = rgeom(n, prob)
    table(y)
    fit = vglm(y ~ x1 + x2 + x3, geometric, trace=TRUE, crit="coef")
    coef(fit)
    coef(fit, mat=TRUE)
    summary(fit)

[Package VGAM version 0.7-9 Index]