faithful: Faithful Dataset

In mixComp: Estimation of Order of Mixture Distributions

Description

Waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA from datasets.

Usage

data(faithful)

Format

A data frame with 272 observations on 2 variables:

eruptions

numeric, eruption time in mins

waiting

numeric, waiting time to next eruption (in mins)

Source

1. Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful geyser. Applied Statistics, 39, 357–365.

2. datasets

Examples

data(faithful)

faithful.obs <- faithful$waiting

# function giving the j^th raw moment of the standard normal distribution,
# needed for calculation of the Hankel matrix via the "translation" method
# (assuming gaussian components with variance 1)
mom.std.norm <- function(j){
  ifelse(j %% 2 == 0, prod(seq(1, j - 1, by = 2)), 0)
}

# generate list of parameter bounds
norm.bound.list <- list("mean" = c(-Inf, Inf), "sd" = c(0, Inf))

# define the MLE functions for the mean and sd: 
MLE.norm.mean <- function(dat) mean(dat)
MLE.norm.sd <- function(dat){
sqrt((length(dat) - 1) / length(dat)) * sd(dat)
} 
MLE.norm.list <- list("MLE.norm.mean" = MLE.norm.mean, "MLE.norm.sd" = MLE.norm.sd)

# construct a 'datMix' object that summarizes all the necessary information:
faithful.dM <- datMix(faithful.obs, dist = "norm", discrete = FALSE,
                      theta.bound.list = norm.bound.list,
                      MLE.function = MLE.norm.list, Hankel.method = "translation",
                      Hankel.function = mom.std.norm)

# estimate the number of components and plot the results:
res <- hellinger.cont(faithful.dM, bandwidth = 4,
                      sample.n = 5000, threshold = "AIC")
plot(res)

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