ParamFamily: Generating function for ParamFamily-class

In distrMod: Object Oriented Implementation of Probability Models

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, startPar returns a search interval, else it returns an initial parameter value.
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 parameter value out of the illegal one; if NULL slot makeOKPar of ParamFamily is used to produce it.
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

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) }.

Value

Object of class "ParamFamily"

Author(s)

Matthias Kohl [e-mail],
Peter Ruckdeschel [e-mail]

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,
          .returnClsName = "ParamWithScaleFamParameter"),
          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,
                                 .returnClsName = "ParamWithScaleFamParameter"),
          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. Exponential scale family
theta <- 2
names(theta) <- "scale"
ES <- ParamFamily(name = "Exponential scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta,
                           .returnClsName = "ParamWithScaleFamParameter"),
          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

## 7. Lognormal scale family
theta <- 2
names(theta) <- "scale"
LS <- ParamFamily(name = "Lognormal scale family",
          param = ParamFamParameter(name = "scale parameter", main = theta,
                           .returnClsName = "ParamWithScaleFamParameter"),
          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

## 8. Gamma family
theta <- c(1, 2)
names(theta) <- c("scale", "shape")
G <- ParamFamily(name = "Gamma family",
        param = ParamFamParameter(name = "scale and shape", main = theta,
                           withPosRestr = TRUE,
                           .returnClsName = "ParamWithScaleAndShapeFamParameter"),
        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

distrMod documentation built on Jan. 12, 2025, 3:01 a.m.