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 0.7-7 Index]