erlang {VGAM}R Documentation

Erlang Distribution

Description

Estimates the scale parameter of the Erlang distribution by maximum likelihood estimation.

Usage

erlang(shape.arg, link = "loge", earg=list(), method.init = 1)

Arguments

shape.arg The shape parameter. The user must specify a positive integer.
link Link function applied to the (positive) scale parameter. See Links for more choices.
earg List. Extra argument for the link. See earg in Links for general information.
method.init An integer with value 1 or 2 which specifies the initialization method. If failure to converge occurs try the other value.

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*scale and its variance is shape*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

The rate parameter found in gamma2.ab is 1/scale here—see also rgamma.

Author(s)

T. W. Yee

References

Most standard texts on statistical distributions describe this distribution, e.g.,

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

See Also

gamma2.ab, exponential.

Examples

n = 200; rate = 8
y = rep(0, n)
for(i in 1:3)
    y = y + rexp(n, rate=rate)
fit = vglm(y ~ 1, erlang(shape=3), trace=TRUE) 
coef(fit, matrix=TRUE)
Coef(fit) # Answer = 1/rate
1/rate
summary(fit)

[Package VGAM version 0.7-7 Index]