# perks: Perks Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

## Description

Maximum likelihood estimation of the 2-parameter Perks distribution.

## Usage

 ```1 2 3 4``` ```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`.

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.

`dperks`, `simulate.vlm`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## 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) ```