My Erdos Number is 3 based on the sequence

• Erdos, P. and Galambos, J. Proc. Amer. Math. Soc. 46 pp. 1-8 (1974).
• Galambos, J. and Seneta, E. Proc. Amer. Math. Soc. 50 pp. 383 - 387(1975).
• Hoppe, F.M. and Seneta, E. Internat. Statist. Rev. 58 pp. 253 - 261(1991).

Selected Recent Publications and Preprints

• S. N. Ethier and Fred M. Hoppe. A world record in Atlantic City and the length of the shooter's hand at craps. The Mathematical Intelligencer, 32 No. 4, pp. 44 - 48. (2010)
• Fred M. Hoppe. Effect of redundancy on probability bounds. Discrete Math. 309 pp. 123-127 (2009)
• Fred M. Hoppe. Faa di Bruno's formula and the distributions of random partitions in population genetics and physics. Theoretical Population Biology. 73 pp. 543 - 551 (2008)
• Fred M. Hoppe and Mikhail Nediak. Frechet optimal bounds on the probability of a union with supplementary information. Statist. Probab. Lett., 78 pp. 511-319 (2008)
• Fred M. Hoppe, Branching processes and the effect of parlaying bets on lottery odds. In Optimal Play: Mathematical Studies of Games and Gambling, Institute for the Study of Gambling and Commercial Gaming, University of Nevada, pp. 361 - 373 (2007).

Recent Refereed Conference Proceedings

• Fred M. Hoppe and Jovica Riznic. Bayesian determination of sample sizes for inspections of feeder hangers. Proceedings of the 17th International Conference on Nuclear Engineering. Brussels, Belgium, July 12 - 16 (2009)
• Fred M. Hoppe and Lin Fang. Bayesian prediction for the Gumbel distribution applied to feeder pipe thicknesses. Proceedings of the 16th International Conference on Nuclear Engineering. Orlando FL, May 11 - 15 (2008)

Current Graduate Students

Xingli Wei (Ph.D.)
Dan Quach (Ph.D.)

Consulting

I am very interested in applications of probability and statistics to industry and business. The main companies with whom I have collaborated are in the nuclear sector and include AMEC-NSS, Nuclear Safety Solutions, Ontario Power Generation, and the former Ontario Hydro, but I have also done work for the Ontario Lottery and Gaming Corporation, the Western Canada Lottery Corporation, the Canadian Nuclear Safety Commission, CANDU Owners Group, Monserco, Ontario Workplace Safety Insurance Board, Kraft Foods, Nestles, and the Ontario College of Respitatory Therapists, as well as various law firms.
I welcome queries from the public.

Lotteries

Since the Maclean's Magazine article appeared, quoting my calculations for Lotto, and comparing the chance of winning to the chance of tossing 24 heads in a row (This description covered Lotto 6/49 at the time. It needs to be updated for the new prize structure.) I have often been contacted by the media when there is lottery fever or some lottery question. This happened most recently in October 2006 the day of a CBC Fifth Estate program concerning allegations of fraud by lottery retailers. I was quoted by the Toronto Star as saying that no more than about 20 retailers should have won major prizes. (This story even appeared in the Canadian Chinese press.)

I computed this number based on the information given to me by both the Star and CHTV. My understanding was that the figures supplied applied only to Lotto Super 7 and my estimate therefore only applied to this particular lottery. Unfortunately, this information was omitted from the article, but happily, the article did say that my conclusion "depend[ed] on assumptions made about how many retailers play the lottery."

A Few Lottery Clips in the Media

Chance

Chance is an outstanding source of probability and statistics ideas as applied to everyday life to which I've occasionally contributed items with pedagogic value. Here are four that would be of interest to high school and university students.

• CHANCE News 6.13
• CHANCE News 7.07
• CHANCE News 9.08
• CHANCE News 9.11

Excel

I am a strong proponent of the use of Excel in teaching undergraduate statistics. Even in my consulting, I have found Excel to be a handy tool for scientists and engineers for examining data, plotting, and suggesting models. Of course, Excel does have some known problems, for instance in simulation. I have written a number of macros for use in my Statistics 1cc3 classes at McMaster University. This archive of macros accompanies the 4th edition of my Excel Manual for The Basic Practice of Statistics, W. H. Freeman, NY, 2006 used in conjunction with David Moore's popular The Basic Practice of Statistics, W. H. Freeman, NY, 2006. The regression to the mean macro S1cc3_corr.xls simulates 1000 pairs of observations (x, y) from a population with a correlation given by a parameter "rho" (Greek letter). It draws the line of equal percentiles and also the regression line. The user can change the value of rho with the slider. Each time the sample is taken, the value of the correlation r computed from the sample is shown. Observe that r is close to rho but does vary from sample to sample. Repeated use of macro shows how scatterplots with different correlations might appear. The sampling simulation macro samsim.xls showing histograms of 1000 SRSs of size 100 from a population. User can change the population proportion. The macro gbmsim.xls simulates stock market prices using geometric Brownian motion.
If you have any questions or suggestions for other macros please contact me. (If you encounter a run-time error in the boxplot macro using the RUN button, then access the macro from the menu Tools --> Macros --> bp--- open_dialog_box.)