| erlang {VGAM} | R Documentation |
Erlang Distribution
Description
Estimates the scale parameter of the Erlang distribution by maximum likelihood estimation.
Usage
erlang(shape.arg, lscale = "loglink", imethod = 1, zero = NULL)
Arguments
shape.arg |
The shape parameters.
The user must specify a positive integer,
or integers for multiple responses.
They are recycled |
lscale |
Link function applied to the (positive) |
imethod, zero |
See |
Details
The Erlang distribution is a special case of
the gamma distribution
with shape that is a positive integer.
If shape.arg = 1
then it simplifies to the exponential distribution.
As illustrated
in the example below, the Erlang distribution is
the distribution of
the sum of shape.arg independent and
identically distributed
exponential random variates.
The probability density function of the Erlang distribution is given by
f(y) = \exp(-y/scale)
y^{shape-1} scale^{-shape} / \Gamma(shape)
for known positive integer shape,
unknown scale > 0 and y > 0.
Here,
\Gamma(shape) is the gamma
function, as in gamma.
The mean of Y
is \mu=shape \times scale and
its variance is shape \times scale^2.
The linear/additive predictor, by default, is
\eta=\log(scale).
Value
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions
such as vglm
and vgam.
Note
Multiple responses are permitted.
The rate parameter found in gammaR
is 1/scale here—see also rgamma.
Author(s)
T. W. Yee
References
Most standard texts on statistical distributions describe this distribution, e.g.,
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
See Also
gammaR,
exponential,
simulate.vlm.
Examples
rate <- exp(2); myshape <- 3
edata <- data.frame(y = rep(0, nn <- 1000))
for (ii in 1:myshape)
edata <- transform(edata, y = y + rexp(nn, rate = rate))
fit <- vglm(y ~ 1, erlang(shape = myshape), edata, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit) # Answer = 1/rate
1/rate
summary(fit)