VGAM (version 0.7-8)

exponential: 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.

Value

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

Details

The family function assumes the response $Y$ has density $$f(y) = \lambda \exp(-\lambda (y-A))$$ for $y > A$, where $A$ is the known location parameter. By default, $A=0$. Then $E(Y) = A + 1/ \lambda$ and $Var(Y) = 1/ \lambda^2$.

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)