compdist: Creates an Object Representing Composite Distribution

In mistr: Mixture and Composite Distributions

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 class 'dist'
compdist(..., weights, breakpoints, break.spec, all.left = FALSE)

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

Arguments

...	distribution objects.
weights	vector of weights for the components.
breakpoints	vector of breakpoints for the composite models, first and last breakpoints (-∞, ∞) 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 -∞ and ∞ 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)=∑ 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.

Value

Object of class compdist.

See Also

mixdist

Examples

# 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

mistr documentation built on March 7, 2023, 7:42 p.m.