Hi everyone! My name is Lauren and I’m a current senior. I will be presenting next Wednesday, March 17 at 2:10. For a brief introduction to what I will be talking about, consider the following hypothetical situation:

Let’s consider the students at Canisius College, and assume there are 2,000 students with an average height of 5.5 ft. If Canisius College begins an foreign exchange program with a distant alien planet, there could potentially (ridiculousness aside) be an alien student at Canisius College that is two miles tall. With the inclusion of this one student in the height statistics, the new average height of Canisius students is about ten feet and nine inches. Is this unreasonable? You would then anticipate an outsider of Canisius College to look around campus and see every student to be about ten feet and nine inches. This outsider would be disappointed (or relieved) to look and see this is not the case. So the question becomes should this new student be included in the average height data if their height qualifies them as an outlier? Likely, the answer is no, for logical reasons. By contrast, consider a major financial corporation, and the new student two miles tall represents an unexpected, unexplainable event that has the potential to drain company assets and bankrupt it. Financial analysts would want to consider the possibility of something like this occurring because of the significant impacts that it would pose. Events that are unlikely, but not impossible, can still occur.

My presentation will focus on extreme events and the types of probability distributions that we would be better off predicting extremes with: stable distributions. An introduction to the types of stable distributions, and then specifically the Cauchy distribution will be made. Applications of these distributions will be shown through R-Studio output of financial data, which will serve as a visual of a Black Swan event. A majority of this presentation will pull from the work of Dr. Nassim Nicholas Taleb, who has devoted his post-financial industry life to mathematical philosophy applied to probability and randomness. It is beneficial to have taken Probability and Statistics 1 & 2, but not a requirement, as some basics will be explained.

A special thank you to Dr. Leonid Khinkis, whose advice and knowledge of these fields has been extremely helpful in guiding me though this work.

” I liked it ” is how I would end this comment if it were permissible.

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I don’t have to many questions, just a couple things to think about. If one takes on your idea of extreme values, what if that is applied to the wider tails. Could there be such distributions where the concavity of the switches? Or what about a distribution system that is the complete opposite of the normal distribution; have most of the data be at the two extremes and very little if not any in the middle to possibly check to see if something like are wage gap is headed towards a pattern as such. Which would probably not be a good thing. The distribution function would then be something that looks like x^2 instead of -x^2.

I am only new to stocks as of last year, but from my experience there has been a decent amount of companies that are just started to figure out how to expand exponentially instead of linear. There has also been a rise in cryptocurrency which I believe may be the next big step for the marketplace. Bitcoin has taken over the markets. In the past 5 years it has risen in value a little over 14,000%. With about four fifths of that growth coming with the last year. So if I mined 20 bucks worth of bitcoin 5 years ago it would be worth $280,000 right now. From what I have learned is that the only limit to how high it is capable of going is based on how many people own it. All it was when it first started was people with computers having a counter that increased at a certain rate and now it is worth something because so many people have it. It is very hard to mine bitcoin today because of its popularity and one needs a very expensive computer or else someone with faster computer will get it first because it is based off scarcity. Only so much is given out per period.

Two PhD students actually started there own currency that they are working on getting more accessible to the daily hands like how robinhood did with more people being able to buy stocks. They created an app called pi where you are able to mine there new currency called “pi”. All you have to do is login in every 24 hours to start mining. They go more into on there app but they are having planned reductions of everyones earning rate by half once they hit certain amount of people who join to create scarcity. It becomes harder to earn more the longer you wait to get some.

sorry if i went on a little tangent

Overall this was a nicely done presentation. I do not know to much about statistics but I found the different properties of distributions and their tails to be very interesting, especially the one that you are told to “forget about”.

I thought your presentation was excellent! I found the topic very interesting, and despite having taken several statistics classes, almost all of the information in your presentation was new to me, which was really great. I enjoyed the examples you provided, as they helped to clarify your main points. I’ve never heard of the “dot com bubble/crash” before, and I thought that was really fascinating. Also, I can’t help but wonder whether or not the pandemic could be considered a black swan event. It’s no question that the pandemic certainly took the economy by storm, but I’m just not sure whether or not it would meet all the criteria you mentioned for it to be considered a black swan event. Also, I really enjoyed your abstract by the way. It was very clever! Amazing job, Lauren! Thanks for sharing such an interesting presentation!

Statistics isn’t my strong suit, but by how you presented your information, it was easy for me to follow along. The examples that you provided a better understanding of the points that you were trying to get across. Also, your abstract really caught my attention and made me look forward to you presentation and I was not disappointed.

I thought your presentation was great. You delivered the information in a clear manner which made it easy for me to understand. Most of the information you were talking about was new to me because I haven’t taken any statistics class. However, through your clear explanations and your example about the student who was 2 miles high, I was able to follow along. I really appreciated the example because when you started discussing extreme events, I kept referring back to it to help me understand what you were talking about.

Hey Lauren! Great job on your presentation. I found your research on Stable Distributions: Extreme Values in the Real World very interesting and informative. It was a well written and well-organized presentation, although I am not good at statistics, it was easy to what you were saying during your presentation, and additionally, you also provided examples, and it was so kind of you. Thank you for the information, and looking forward to your future research development.

This was absolutely awesome. I read The Black Swan by Taleb about 2 years ago and it was truly one of the most eye-opening books I’ve ever read. You did a great job of breaking down some complex statistical ideas. Even having taken Statistics 2, there were some parts that I didn’t quite remember or maybe we just didn’t learn, and yet I did not feel lost.