distrMod (version 2.0.7)

ParamFamily: Generating function for ParamFamily-class

Description

Generates an object of class "ParamFamily".

Usage

ParamFamily(name, distribution = Norm(), distrSymm, modifyParam,
            main = main(param), nuisance = nuisance(param),
            fixed = fixed(param), trafo = trafo(param),
            param = ParamFamParameter(name = paste("Parameter of", 
                          name),  main = main, nuisance = nuisance, 
                                  fixed = fixed, trafo = trafo),
            props = character(0),
            startPar = NULL, makeOKPar = NULL)

Arguments

name

character string: name of family

distribution

object of class "Distribution": member of the family

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

startPar

startPar is a function in the observations x returning initial information for MCEstimator used by optimize resp. optim; i.e; if (total) parameter is of length 1, star

makeOKPar

makeOKPar is a function in the (total) parameter param; used if optim resp. optimize--- try to use ``illegal'' parameter values; then makeOKPar makes a valid par

main

numeric vector: main parameter

nuisance

numeric vector: nuisance parameter

fixed

numeric vector: fixed part of the parameter

trafo

function in param or matrix: transformation of the parameter

param

object of class "ParamFamParameter": parameter of the family

modifyParam

function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

character vector: properties of the family

Value

• Object of class "ParamFamily"

concept

parametric family

Details

If name is missing, the default "parametric family of probability measures" is used. In case distrSymm is missing it is set to NoSymmetry(). If param is missing, the parameter is created via main, nuisance and trafo as described in ParamFamParameter. One has to specify a function which represents a mapping from the parameter space to the corresponding distribution space; e.g., in case of normal location a simple version of such a function would be function(theta){ Norm(mean = theta) }.

See Also

ParamFamily-class

Examples

## "default" (normal location)
F1 <- ParamFamily(modifyParam = function(theta){ Norm(mean = theta) })
plot(F1)

################################
## Some examples:
################################
## 1. Normal location family
theta <- 0
names(theta) <- "mean"
NL <- ParamFamily(name = "Normal location family",
          param = ParamFamParameter(name = "location parameter", main = theta),
          distribution = Norm(mean = 0, sd = 1), ## sd known!
          startPar = function(x,...) c(min(x),max(x)),
          distrSymm <- SphericalSymmetry(SymmCenter = 0),
          modifyParam = function(theta){ Norm(mean = theta, sd = 1) },
          props = paste(c("The normal location family is invariant under",
                    "the group of transformations 'g(x) = x + mean'",
                    "with location parameter 'mean'"), collapse = ""))
NL

## 2. Normal scale family
theta <- 1
names(theta) <- "sd"
NS <- ParamFamily(name = "Normal scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta),
          distribution = Norm(mean = 0, sd = 1), ## mean known!
          startPar = function(x,...) c(0,-min(x)+max(x)),
          distrSymm <- SphericalSymmetry(SymmCenter = 0),
          modifyParam = function(theta){ Norm(mean = 0, sd = theta) },
          props = paste(c("The normal scale family is invariant under",
                    "the group of transformations 'g(y) = sd*y'",
                    "with scale parameter 'sd'"), collapse = ""))
NS

## 3. Normal location and scale family
theta <- c(0, 1)
names(theta) <- c("mean", "sd")
NLS <- ParamFamily(name = "Normal location and scale family",
          param = ParamFamParameter(name = "location and scale parameter",
                                    main = theta),
          distribution = Norm(mean = 0, sd = 1),
          startPar = function(x,...) c(median(x),mad(x)),
          makeOKPar = function(param) {param[2]<-abs(param[2]); return(param)},
          distrSymm <- SphericalSymmetry(SymmCenter = 0),
          modifyParam = function(theta){
                            Norm(mean = theta[1], sd = theta[2])
                        },
          props = paste(c("The normal location and scale family is",
                    "invariant under the group of transformations",
                    "'g(x) = sd*x + mean' with location parameter",
                    "'mean' and scale parameter 'sd'"),
                    collapse = ""))
NLS

## 4. Binomial family
theta <- 0.3
names(theta) <- "prob"
B <- ParamFamily(name = "Binomial family",
         param = ParamFamParameter(name = "probability of success", 
                                   main = theta),
         startPar = function(x,...) c(0,1),
         distribution = Binom(size = 15, prob = 0.3), ## size known!
         modifyParam = function(theta){ Binom(size = 15, prob = theta) },
         props = paste(c("The Binomial family is symmetric with respect",
                   "to prob = 0.5; i.e.,",
                   "d(Binom(size, prob))(k)=d(Binom(size,1-prob))(size-k)"),
                   collapse = ""))
B

## 5. Poisson family
theta <- 7
names(theta) <- "lambda"
P <- ParamFamily(name = "Poisson family",
          param = ParamFamParameter(name = "positive mean", main = theta),
          startPar = function(x,...) c(0,max(x)),
          distribution = Pois(lambda = 7),
          modifyParam = function(theta){ Pois(lambda = theta) })
P

## 6. Gumbel location family
theta <- 0
names(theta) <- "loc"
GL <- ParamFamily(name = "Gumbel location family",
          param = ParamFamParameter(name = "location parameter", main = theta),
          startPar = function(x,...) c(min(x),max(x)),
          distribution = Gumbel(loc = 0, scale = 1), ## scale known!
          modifyParam = function(theta){ Gumbel(loc = theta, scale = 1) },
          props = paste(c("The Gumbel location family is invariant under",
                    "the group of transformations 'g(x) = x + loc'",
                    "with location parameter 'loc'"), collapse = ""))
GL

## 7. Exponential scale family
theta <- 2
names(theta) <- "scale"
ES <- ParamFamily(name = "Exponential scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta),
          startPar = function(x,...) c(0,max(x)-min(x)),
          distribution = Exp(rate = 1/2),
          modifyParam = function(theta){ Exp(rate = 1/theta) },
          props = paste(c("The Exponential scale family is invariant under",
                    "the group of transformations 'g(y) = scale*y'",
                    "with scale parameter 'scale = 1/rate'"),
                    collapse = "" ))
ES

## 8. Lognormal scale family
theta <- 2
names(theta) <- "scale"
LS <- ParamFamily(name = "Lognormal scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta),
          startPar = function(x,...) c(0,max(x)-min(x)),
          distribution = Lnorm(meanlog = log(2), sdlog = 2),## sdlog known!
          modifyParam = function(theta){ 
                            Lnorm(meanlog = log(theta), sdlog = 2) 
                        },
          props = paste(c("The Lognormal scale family is invariant under",
                    "the group of transformations 'g(y) = scale*y'",
                    "with scale parameter 'scale = exp(meanlog)'"),
                    collapse = ""))
LS

## 9. Gamma family
theta <- c(1, 2)
names(theta) <- c("scale", "shape")
G <- ParamFamily(name = "Gamma family",
        param = ParamFamParameter(name = "scale and shape", main = theta),
        startPar = function(x,...) {E <- mean(x); V <- var(X); c(V/E,E^2/V)},
        makeOKPar = function(param) abs(param),
        distribution = Gammad(scale = 1, shape = 2),
        modifyParam = function(theta){ 
                          Gammad(scale = theta[1], shape = theta[2]) 
                      },
        props = paste(c("The Gamma family is scale invariant via the",
                  "parametrization '(nu,shape)=(log(scale),shape)'"),
                  collapse = ""))
G