OptInterim (version 3.0.1)

weibPmatch: Compute the shape or scale parameter for a Weibull distribution so it has a specified event-free rate at a specified time.

Description

Determine the shape or scale parameter of a Weibull distribution so it has event-free rate P0 at time x. If the shape is specified, the scale parameter is computed, and if the scale is specified, the shape parameter is computed.

Usage

weibPmatch(x, p0, shape, scale)

Arguments

x

Pre-specified time for the event-free endpoint (e.g., 1 year).

p0

Event-free rate at time x.

shape

If specified, the necessary scale parameter is computed

scale

If specified, the necessary shape parameter is computed

Value

A single numerical value is returned, either the shape or scale parameter, depending on which is specified by the user.

Details

The time and event-free rate must be supplied. Either the shape or scale parameter must also be specified, but not both. The R parameterization of the Weibull distribution is used.

References

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.

See Also

weibull.plot,pweibull, OptimDes

Examples

param <- c(1, 1.09, 2, 1.40)
x<-1

p0<-pweibull(x,param[1],param[2],lower=FALSE)
p1<-pweibull(x,param[3],param[4],lower=FALSE)

weibull.plot(param,x)

### equivalent to simple call
paramNew<-c(param[1], weibPmatch(x,p0,param[1]), param[3], weibPmatch(x,p1,param[3]))
weibull.plot(paramNew, x)

### null curve with different shape
paramNew<-c(3.0, weibPmatch(x,p0,3.0), param[3], weibPmatch(x,p1,param[3]))
weibull.plot(paramNew, x)

### alternative curve with different scale
paramNew<-c(param[1], param[2], weibPmatch(x,p1,scale=2), 2)
weibull.plot(paramNew, x)