R: Perks Distribution Family Function

perks {VGAM} | R Documentation

## Perks Distribution Family Function

### Description

Maximum likelihood estimation of the 2-parameter Perks distribution.

### Usage

    perks(lscale = "loglink", lshape = "loglink",
          iscale = NULL,   ishape = NULL,
          gscale = exp(-5:5), gshape = exp(-5:5),
          nsimEIM = 500, oim.mean = FALSE, zero = NULL, nowarning = FALSE)

### Arguments

`nowarning` | Logical. Suppress a warning? Ignored for VGAM 0.9-7 and higher.
`lscale, lshape` | Parameter link functions applied to the shape parameter `shape`, scale parameter `scale`. All parameters are treated as positive here See `Links` for more choices.

`iscale, ishape` | Optional initial values. A `NULL` means a value is computed internally.
`gscale, gshape` | See `CommonVGAMffArguments`.
`nsimEIM, zero` | See `CommonVGAMffArguments`.
`oim.mean` | To be currently ignored.

### Details

The Perks distribution has cumulative distribution function

F(y; alpha, beta) = 1 - ((1 + α)/(1 + alpha * e^(beta * y)))^(1 / beta)

which leads to a probability density function

f(y; alpha, beta) = [ 1 + alpha]^(1 / β) * alpha * exp(beta * y) / (1 + alpha * exp(beta * y))^(1 + 1 / beta)

for alpha > 0, beta > 0, y > 0. Here, beta is called the scale parameter `scale`, and alpha is called a shape parameter. The moments for this distribution do not appear to be available in closed form.

Simulated Fisher scoring is used and multiple responses are handled.

### Value

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

### Warning

A lot of care is needed because this is a rather difficult distribution for parameter estimation. If the self-starting initial values fail then try experimenting with the initial value arguments, especially `iscale`. Successful convergence depends on having very good initial values. Also, monitor convergence by setting `trace = TRUE`.

### Author(s)

T. W. Yee

### References

Perks, W. (1932). On some experiments in the graduation of mortality statistics. Journal of the Institute of Actuaries, 63, 12–40.

Richards, S. J. (2012). A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal. 1–25.

### See Also

`dperks`, `simulate.vlm`.

### Examples

    ## Not run:  set.seed(123)
    pdata <- data.frame(x2 = runif(nn <- 1000))  # x2 unused
    pdata <- transform(pdata, eta1  = -1,
                              ceta1 =  1)
    pdata <- transform(pdata, shape1 = exp(eta1),
                              scale1 = exp(ceta1))
    pdata <- transform(pdata, y1 = rperks(nn, shape = shape1, scale = scale1))
    fit1 <- vglm(y1 ~ 1, perks, data = pdata, trace = TRUE)
    coef(fit1, matrix = TRUE)
    summary(fit1)

    ## End(Not run)

[Package VGAM version 1.1-3 Index]