perks: Perks Distribution Family Function

In VGAM: Vector Generalized Linear and Additive Models

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 - \left\{ \frac{1 + \alpha}{1 + \alpha e^{\beta y}} \right\}^{1 / \beta}

which leads to a probability density function

f(y; \alpha, \beta) = \left[ 1 + \alpha \right]^{1 / \beta} \alpha e^{\beta y} / (1 + \alpha e^{\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, sh = shape1, sc = scale1))
fit1 <- vglm(y1 ~ 1, perks, data = pdata, trace = TRUE)
coef(fit1, matrix = TRUE)
summary(fit1)

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.