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The Asymptotic Normality Of Total Claims

The purpose of this video is to make a case for the asymptotic normality of the total claim amount for an insurance company. This will involve giving a brief history of the Central Limit Theorem, explaining how it looks in practice, discussing Lindeberg's version of it, illustrating Lindeberg's version, and then drawing the appropriate conclusion. (0:00:00) Introduction (0:11:05) Examples (0:20:12) Rates Of Convergence (0:25:06) Examples (cont.) (0:26:02) Lindeberg's Version (0:36:44) Simulation Of Different Distributions (0:44:25) Conclusion References 1. Spheeris, Penelope, director. Black Sheep. Screenplay by Fred Wolf. Paramount Pictures, 1996. Timestamp: 00.00 2. Pagan's Mind. "God's Equation." God's Equation, Limb Music, 2007. Timestamp: 00.08 3. Reed, Carol, director. Oliver!. Screenplay by Vernon Harris. Columbia Pictures, 1996. Timestamp: 05.10 4. Pólya, Georg 1920. Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem. Mathematische Zeitschrift 8, 171–181. Timestamp: 05.25 5. de Moivre, Abraham 1733. Approximatio ad summam terminorum binomii .a C b/n in seriemexpansi. 7 pages offprint. Timestamp: 05.54 6. Laplace, Pierre-Simon 1812. Théorie analytique des probabilités. Book 2, chapter 4. Timestamp: 06.50 7. Fischer, Hans. A History Of The Central Limit Theorem: From Classical To Modern Probability Theory. New York: Springer, 2011. Timestamp: 07.15 8. Lindeberg, J. W. 1922. "Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung". Mathematische Zeitschrift. 15, 211–225. Timestamp: 08.31 9. Mourier, Edith 1953a. Éléments aléatoires dans un espace de Banach. Annales de l’Institut Henri Poincaré 13, 161–244. Timestamp: 08.47 10. Le Cam, Lucien. “The Central Limit Theorem Around 1935.” Statistical Science 1, no. 1 (1986): 78–96. Timestamp: 09.27 11. Crichton, Charles, director. A Fish Called Wanda. Screenplay by John Cleese. MGM / UA Communications Co., 1988. Timestamp: 19.21 12. Esseen, Carl-Gustav - On The Liapounoff Limit Of Error In The Theory Of Probability. Ark. Mat. Astr. Fys. 28A, (1942), no. 9, 19 pp. Timestamp: 23.00 13. Berry, Andrew C. - The Accuracy Of The Gaussian Approximation To The Sum Of Independent Variates Trans. Amer. Math. Soc. 49 (1941), 122-136. Timestamp: 23.05 14. P. van Beek (1972) An Application Of Fourier Methods To The Problem Of Sharpening The Berry - Esseen inequality. Z. Warsch. verw. Gebiete. 23, 187–196. Timestamp: 24.22 15. P. Hall (1982) Rates Of Convergence In The Central Limit Theorem. Timestamp: 24.27 16. Violent Femmes. (2005). Add It Up. Permanent Record: Live & Otherwise. New York, NY: Rhino Entertainment. Timestamp: 40.20 17. Yankovic, Alfred. “Weird Al.” (1988). I Think I’m a Clone Now. Even Worse. Scotti Brothers Records. Timestamp: 46.51 18. Studio Service. (1998). I Think I’m a Clone Now (Kaysow extended remake). Based on Neon Genesis Evangelion and the song “I Think I’m a Clone Now” by “Weird Al” Yankovic. Timestamp: 46.59