children: Children Dataset

In mixComp: Estimation of Order of Mixture Distributions

Description

Number of children of 4075 widows entitled to support from a certain pension fund from Thisted (1988).

Usage

data(children)

Format

A data frame with 4075 observations on 1 variable. Replicates are generated to reflect the number of children n that widows entitled to support have (n = 0, 1, ..., 6). As there are 3062 widows that have no children, 0 appears 3062 times in the data, as there are 587 widows that have one child, 1 appears 587 times in the data, etc.

Source

Thisted, R. A. (1988). Elements of statistical computing: Numerical computation (Vol. 1). CRC Press.

Examples

data(children)

# convert the data to vector:
children.obs <- unlist(children)

# explicit function giving the estimate for the j^th moment of the
# mixing distribution, needed for Hankel.method "explicit"
explicit.pois <- function(dat, j){
  mat <- matrix(dat, nrow = length(dat), ncol = j) -
         matrix(0:(j-1), nrow = length(dat), ncol = j, byrow = TRUE)
  return(mean(apply(mat, 1, prod)))
}

# define the MLE function:
MLE.pois <- function(dat) mean(dat)

# construct a 'datMix' object:
children.dM <- datMix(children.obs, dist = "pois", discrete = TRUE,
                      Hankel.method = "explicit",
                      Hankel.function = explicit.pois,
                      theta.bound.list = list(lambda = c(0, Inf)),
                      MLE.function = MLE.pois)
                      
# define the penalty:
pen <- function(j, n) j * log(n)

# complexity estimation:

set.seed(0)
det_sca_pen <- nonparamHankel(children.dM, j.max = 5, scaled = TRUE,
                               B = 1000, pen.function = pen)
plot(det_sca_pen, main = "Non-parametric Hankel method for Children dataset")

mixComp documentation built on Feb. 25, 2021, 5:07 p.m.