Mažųjų skaičių dėsnis: L. Bortkievičiaus duomenų analizė /

Although probability theory and statistics are some of the most challenging areas of mathematical science, their methods make it possible to work as efficiently as possible with all kinds of data, which are abundant, starting from their processing to their presentation. Different laws and distributions are found in probability theory, and we will try to analyze one of them in detail in this paper. It is evident from the topic that the subject matter pertains to "The Law of Small Numbers" (LSN). However, in addition to everything, it is not as widespread and prevalent as the "Law of Large Numbers" (LLN) that everyone, more or less, knows or has heard at least once in their life. What is LSN, and does it exist? Unfortunately, if we were to ask Google in Lithuanian, we would find an answer. Even some scientists think that the law is nothing more than an isolated case of the Poisson distribution or even human error associated with LLN. However, it turns out that this is one of the most necessary principles to understand the most common mistakes in statistics and to correctly interpret data of various sizes, especially those related to rare or unlikely phenomena. In addition, it also reveals that small samples may exhibit more significant random variation compared to larger samples. One of the most famous historical scientists who contributed to the mentioned branch of mathematics, and especially to the emergence of the concept of LSN and the development of its applications, is Ladislaus von Bortkiewicz. His work on the Poisson distribution for rare events, such as the statistics of deaths of Prussian cavalrymen from horse kicks, is still considered a classic example of science. Bortkiewicz not only showed how the theory can be applied in practice but also demonstrated how statistical methods can help to understand the regularity of seemingly chaotic or completely random phenomena. So, further on in this paper, it will be shown that the law is no less significant than its further mentioned "opposite", also, as before, it is a very relevant topic in the real world these days and is widely employed. During the work, we will try to show how these theories work and can be manipulated in modern statistical practice by performing literature and data analysis based on Bortkiewicz's statistics application data sets. Not only does this help to better understand the law itself, its essence, and areas of application, but it also reveals how historical scientific achievements are still relevant and applicable in our time. The reviewed literature includes original publications, articles, varied websites, and educational sources on probability theory and mathematical statistics.

Grantor dc:publisher

Institutional Repository of Vilnius University

Year dc:date

2024

Author dc:creator

• Andrijevskaja, Angelina,

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

lit

Repository record dc:identifier

https://repository.vu.lt/VU:ELABAETD210641597&prefLang=en_US

OAI identifier oai:identifier

oai:vu.lt:elaba:210641597