compdist: Creates an Object Representing Composite Distribution

Description

compdist creates an object which represents the composite distribution.

Usage

compdist(..., weights, breakpoints, break.spec, all.left = FALSE)
# S3 method for dist
compdist(..., weights, breakpoints, break.spec, all.left = FALSE)
# S3 method for default
compdist(dist, params, weights, breakpoints, break.spec, all.left = FALSE, ...)

Value

Object of class compdist.

Arguments

...: distribution objects.
weights: vector of weights for the components.
breakpoints: vector of breakpoints for the composite models, first and last breakpoints ($-\infty$, $\infty$) are assumed to be given, and should not be specified.
break.spec: vector of breakpoints specifications with values "L" or "R", breakpoints specifications corresponding to $-\infty$ and $\infty$ should not be specified.
all.left: if TRUE, all break.spec are set to "L", default: FALSE.
dist: vector of distribution names.
params: list of parameters.

Details

A CDF of a composite distribution function is $$F(A)=\sum w_{i}F_{i}(A|B_{i})$$, where $w_{i}$ is the weight of the i-th component, $F_{i}()$ is the CDF of the i-th component and $B_{i}$ is the interval specified by the breakpoints. Clearly, the composite models are a specific case of the mixture models, where the corresponding probability distribution functions are truncated to some disjoint support.

The objects can be specified in two ways, either the user may enter objects representing distributions or a vector of names and list of parameters. See the examples below.

The argument break.spec defines if the breakpoint should be included to the distribution to the right ("R") or to the left ("L") of the breakpoint. This feature is of course useful only in the case where at least one of the adjacent components is discrete. By default the intervals are left-closed (all break.spec values are "R").

The function permits to use the same breakpoint twice. This possibility allows to define a partition on a singleton, and hence to create a mass of probability. If this feature is used, the break.spec needs to be specified with "R" and "L", for the first and the second identical breakpoints, respectively, or not set at all.

Examples

Run this code

# using the objects
C <- compdist(normdist(1, 3), expdist(4), weights = c(0.7, 0.3), breakpoints = 2)
C

# using the names and parameters
C2 <- compdist(c("norm","exp"), list(c(mean = 1, sd = 3), c(rate = 4)),
              weights = c(0.7, 0.3), breakpoints = 2)
C2

# more complicated model where break.spec is useful
C3 <- compdist(-GPDdist(1,0.15,0.7), normdist(-1,1), binomdist(5,0.5),
              geomdist(0.3) + 2, weights = c(0.075, 0.425, 0.425, 0.075),
              breakpoints = c(-2.5, 0,3), break.spec = c("L", "R", "R"))
C3

# same breakpoint twice
C4 <-  compdist(-expdist(2),poisdist(),expdist(2),
                weights = c(0.25, 0.5, 0.25), breakpoints = c(0, 0))
C4