(Ex. 8.1 in HSAUR, modified for clarity) The data from contains the velocities of 82 galaxies from six well-separated conic sections of space (Postman et al., 1986, Roeder, 1990). The data are intended to shed light on whether or not the observable universe contains superclusters of galaxies surrounded by large voids. The evidence for the existence of superclusters would be the multimodality of the distribution of velocities.(8.1 Handbook)

Construct histograms using the following functions:

-hist() and ggplot()+geom_histogram()

-truehist() and ggplot+geom_histogram() (make sure that the histograms show proportions, not counts.)

-qplot()

new variable = loglog(galaxies). Repeat part a) using the loggalaxies variable. Does this affect your interpretation of the graphs?

Construct kernel density estimates using two different choices of kernel functions and three choices of bandwidth (one that is too large and "oversmooths," one that is too small and "undersmooths," and one that appears appropriate.) Therefore you should have six different kernel density estimates plots (you may combine plots when appropriate to reduce the number of plots made). Discuss your results. You can use the log scale or original scale for the variable, and specify in the plot x-axis which you choose.

What is your conclusion about the possible existence of superclusters of galaxies? How many superclusters (1, 2, 3, ... )? (Hint: the existence of clusters implies the existence of empty spaces between galaxies.)

Fit a finite mixture model using the Mclust() function in R (from the mclust library). How many clusters did it find? Did it find the same number of clusters as your graphical inspection? Report parameter estimates and BIC of the best model.