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

• Stewart N. Ethier and Fred M. Hoppe. Teaching a University Course on the Mathematics of Gambling. UNLV Gaming Research & Review Journal. Retrieved from https://digitalscholarship.unlv.edu/grrj/vol24/iss1/2. 24(1), pp. 1 - 35 (2020).
• Fred M. Hoppe, Daniel J. Hoppe, and Stephen J. Walter. Explaining odds ratios as conditional risk ratios. Journal of Clinical Epidemiology, 97 pp. 123 - 124 (2018).
• Fred M. Hoppe, Daniel J. Hoppe, and Stephen J. Walter. Odds ratios deconstructed: a new way to understand and explain odds ratios. Journal of Clinical Epidemiology, 82 pp. 87 - 93 (2017).
• Fred M. Hoppe. Benford's Law and distractors in multiple choice exams. International Journal of Mathematical Education in Science and Technology, 47(4), pp. 606 - 612 (2016).
• Daniel J. Hoppe, Matthew Denkers, Fred M. Hoppe, and Ivan H. Wong. The use of video prior to arthroscopic shoulder surgery to enhance patient recall and satisfaction: a randomi\zed-controlled study. Journal of Shoulder and Elbow Surgery, doi:10.1016/jse.2013.09.008, 23(6), pp. 134 - 139 (2014).
  Winner of 2014 Stephen Abrahamson Award for Outstanding Innovation. Innovations in Medical Education Conference 2014, Keck School of Medicine of USC, Los Angeles, February 22 - 23, (2014).
• Paul Sermer, Fred M. Hoppe, Dan-Pun Quach, Keith R. Weaver, Charles Olive,and Israel Cheng. Statistical foundation for decision making in nuclear safety-related problems using best estimate plus uncertainty analyses, Nuclear Science and Engineering, 178, pp. 119 - 155 (2014).
• Fred M. Hoppe and Keith R. Weaver. The happy medium: a useful property of solutions from EVS methodology. Canadian Nuclear Society Bulletin, 34(1), pp. 13 - 17 (2013).
• Dan Pun-Quach, Paul Sermer, Fred M. Hoppe, Oved Nainer, and Bac Phan. A BEPU analysis separating epistemic and aleatory errors to compute accurate dryout power uncertainties. Nuclear Technology, 181, pp. 170 - 183 (2013).
• Fred M. Hoppe and Eugene Seneta. Gumbel's Identity, binomial moments, and Bonferroni sums. International Statistical Review, 80(2), pp. 269 - 292 (2012).
• Stewart 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(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

• D. Quach, P. Sermer, F. M. Hoppe, O. Nainer, and B. Phan. A Best-estimate plus uncertainty type analysis for computing accurate critical channel power uncertainties. Proceedings of The 14th International Topical Meeting on Nuclear Reactor Thermalhydraulics, NURETH-14 Toronto, Ontario, Canada, September 25 - 30, (2011)
• 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/Recent Graduate Students

Dan Pun-quach (Ph.D.) - graduated September 2015. "A Statistical Framework for Distinguishing between Aleatory and Epistemic Uncertainties in the Best-Estimate Plus Uncertainty (BEPU) Nuclear Safety Analyses"
Xingli Wei (Ph.D.) - graduated June 2014. "Parameter Estimation and Prediction Interval Construction for Location-Scale Models with Nuclear Applications"
Jungtae Kim (M.Sc.) - graduated January 2012. "Optimal Strategy Hand-Rank Table for Jacks or Better, Double Bonus, and Joker WildVideo Poker"

Consulting

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

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