exponential {VGAM} | R Documentation

## Exponential Distribution

### Description

Maximum likelihood estimation for the exponential distribution.

### Usage

    exponential(link = "loge", earg = list(), location = 0, expected = TRUE)

### Arguments

`link` | Parameter link function applied to the positive parameter rate. See `Links` for more choices.
`earg` | List. Extra argument for the link. See `earg` in `Links` for general information.
`location` | Numeric of length 1, the known location parameter, A, say.
`expected` | Logical. If `TRUE` Fisher scoring is used, otherwise Newton-Raphson. The latter is usually faster.

### Details

The family function assumes the response Y has density

f(y) = rate * exp(-rate * (y-A))

for y > A, where A is the known location parameter. By default, A=0. Then E(Y) = A + 1/rate and Var(Y) = 1/rate^2.

### Value

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

### Note

Suppose A=0. For a fixed time interval, the number of events is Poisson with mean rate if the time between events has a geometric distribution with mean 1/rate. The argument `rate` in `exponential` is the same as `rexp` etc. The argument `lambda` in `rpois` is somewhat the same as `rate` here.

### Author(s)

T. W. Yee

### References

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

### See Also

`amlexponential`, `laplace`, `poissonff`, `mix2exp`, `freund61`.

### Examples

    nn = 100
    x1 = runif(nn) - 0.5
    x2 = runif(nn) - 0.5
    eta = 0.2 - 0.7 * x1 + 1.9 * x2
    rate = exp(eta)
    y = rexp(nn, rate=rate)
    stem(y)
    fit = vglm(y ~ x1 + x2, exponential, trace=TRUE, crit="c") # slower
    fit = vglm(y ~ x1 + x2, exponential(exp=FALSE), trace=TRUE, crit="c") # faster
    coef(fit)
    coef(fit, mat=TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 0.7-9 Index]