# Generating function for ParamFamily-class Generates an object of class `"ParamFamily"`. ```r 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) }`. ## Returns Object of class `"ParamFamily"` ## Author(s) Matthias Kohl Matthias.Kohl@stamats.de , Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de ## See Also `ParamFamily-class` ## Examples ```r ## "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 ```

ParamFamily function