University of Illinois
College of Business Administration
Department of Information & Decision Sciences
IDS 594:  Special Topics in IDS --  Statistical Finite Mixture Models

Fall Semester, 2002
Prof. Stanley L. Sclove 
Histogram Exercises
1.
     The number of days ill in a year is given for a sample of n = 50 coal miners in the dataset http://www.uic.edu/classes/ids472/data/daysill.txt . Make a series of histograms with various bin widths to illustrate the shape of the distribution, as follows.

One often reasonable rule for the number of bins is that if  n is about   2k,  use  k+1  bins.  Here n = 50, which is between 32 and 64, the fifth and sixth powers of 2.    The rule would suggest six or seven bins.  Using Excel or Minitab, make histograms with 5, 7 and 9 bins.  Compare them.  Which seems to show the overall pattern best ?  Making a succession of histograms with different bin widths can be help in formulating a mixture model for the data.

2.  Stock Rates of Return:  Crude Oil

Given a price series  {P(t)},  the rate of return is  [P(t+1) - P(t)]/P(t), which is approximately  ln P(t+1)/P(t),  or
ln P(t+1) - ln P(t) .  This is often multiplied by 100 to correspond to percent.  This logarithmic approximation to the percentage RORs of the crude-oil nearest month futures prices is in the worksheet  in the column 100*DIFF.   Make histograms of 100*DIFF using bin widths of say, 1.5, 2.0 and 2.5, or whatever best exhibits the information in the data.



created  2002:  May 29       latest update  2002:  July 3