Exponential Distribution
Maximum likelihood estimation for the exponential distribution.
exponential(link = "loglink", location = 0, expected = TRUE,
type.fitted = c("mean", "percentiles", "Qlink"),
percentiles = 50,
ishrinkage = 0.95, parallel = FALSE, zero = NULL)link |
Parameter link function applied to the positive parameter rate.
See |
location |
Numeric of length 1, the known location parameter, A, say. |
expected |
Logical. If |
ishrinkage, parallel, zero |
See |
type.fitted, percentiles |
See |
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.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
T. W. Yee
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
edata <- data.frame(x2 = runif(nn <- 100) - 0.5)
edata <- transform(edata, x3 = runif(nn) - 0.5)
edata <- transform(edata, eta = 0.2 - 0.7 * x2 + 1.9 * x3)
edata <- transform(edata, rate = exp(eta))
edata <- transform(edata, y = rexp(nn, rate = rate))
with(edata, stem(y))
fit.slow <- vglm(y ~ x2 + x3, exponential, data = edata, trace = TRUE)
fit.fast <- vglm(y ~ x2 + x3, exponential(exp = FALSE), data = edata,
trace = TRUE, crit = "coef")
coef(fit.slow, mat = TRUE)
summary(fit.slow)
# Compare results with a GPD. Has a threshold.
threshold <- 0.5
gdata <- data.frame(y1 = threshold + rexp(n = 3000, rate = exp(1.5)))
fit.exp <- vglm(y1 ~ 1, exponential(location = threshold), data = gdata)
coef(fit.exp, matrix = TRUE)
Coef(fit.exp)
logLik(fit.exp)
fit.gpd <- vglm(y1 ~ 1, gpd(threshold = threshold), data = gdata)
coef(fit.gpd, matrix = TRUE)
Coef(fit.gpd)
logLik(fit.gpd)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.