expMeanlink: Link functions for the mean of 1--parameter continuous distributions: The exponential distribution.

Description

Computes the expMeanlink transformation, its inverse and the first two derivatives.

Usage

expMeanlink(theta, location = 0, bvalue = NULL, inverse = FALSE,
                     deriv = 0, short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. This is $\theta$ although may be $\eta$ depending on the other parameters. See below for further details.

location

This is a known location parameter. Same as location in exponential.

bvalue, inverse, deriv, short, tag

See Links.

Value

For deriv = 0, the expMeanlink transformation of theta when inverse = FALSE. If inverse = TRUE, then the inverse exp(theta - A)^(-1).

For deriv = 1, $d$ eta / $d$ theta when inverse = FALSE. If inverse = TRUE, then $d$ theta / $d$ eta as a function of theta.

Similarly, when deriv = 2, the second derivatives in terms of theta are returned.

Details

This is a link function to model the mean of the exponential distribution, exponential. It is defined as $$\eta = \log (A + \lambda^{-1}), $$ where $\lambda > 0$ is a rate parameter and $A$ is a known location parameter, same as exponential.

Numerical values of $\lambda$ out of range may result in Inf, -Inf, NA or NaN.

Examples

Run this code

# NOT RUN {
 ##  E1. Modelling the mean of the exponential distribution  ##
    set.seed(17010402)
    nn <- 100
    edata <- data.frame(x2 = runif(nn) - 0.5, x3 = runif(nn) - 0.5)
    edata <- transform(edata, eta = 0.2 - 0.7 * x2 + 1.9 * x3)
    
            #----- The mean is a function of 'x2' and 'x3' ------#
    edata <- transform(edata, rate = expMeanlink(eta, inverse = TRUE))
    
    edata <- transform(edata, y = rexp(nn, rate = rate))
    with(edata, stem(y))
    with(edata, hist(y))

    exp.fit <- vglm(y ~ x2 + x3, exponential(link = "expMeanlink"), 
                    data = edata, zero = NULL, trace = TRUE, crit = "log")
   coef(exp.fit, matrix = TRUE)
   summary(exp.fit)
 
 ## E2. expMeanlink() and its inverse ##
    theta <- 0.1 + 1:5
    location <- 1.5
    my.diff <- theta - expMeanlink(expMeanlink(theta = theta, 
                  location = location), location = location, inverse  =TRUE)
    summary(my.diff)     # Zero


  ## E3. Special values in a matrix ##
    theta <- matrix(c(Inf, -Inf, NA, NaN, 1 , 2), ncol = 3, nrow = 2)
    expMeanlink(theta = theta, location = location)
# }