Learning about Extreme Value Theory through Simulation

In this video, we use Julia to run Monte Carlo simulations illustrating the Central Limit Theorem and the Fisher-Tippett-Gnedenko theorem. We show that sample averages converge to a Normal distribution, that the maximum of exponential draws converges to a Gumbel distribution, that the maximum of Pareto draws converges to a Fréchet distribution, and that the minimum of exponential draws converges to an Exponential distribution. Slides used in the video are available here: https://raw.githack.com/tyleransom/structural-econ-guy/master/15-ExtremeValueTheory/02-EVT-Simulations.pdf Source code for the slides is here: https://github.com/tyleransom/structural-econ-guy/blob/master/15-ExtremeValueTheory/02-EVT-Simulations.tex Julia simulation script used in this video: https://github.com/tyleransom/structural-econ-guy/blob/master/15-ExtremeValueTheory/CLTillustration.jl Topics covered: - Central Limit Theorem via Monte Carlo simulation - Maximum order statistics and the Gumbel distribution (exponential parent) - Maximum order statistics and the Fréchet distribution (Pareto parent) - Minimum order statistics and the Exponential distribution - Fisher-Tippett-Gnedenko theorem illustrated numerically - Simulation in Julia using the Distributions.jl package Tyler Ransom is an Associate Professor of Economics at the University of Oklahoma. Subscribe for more videos on data science, econometrics, and research methods! #extremevaluetheory #EVT #Gumbeldistribution #Fréchetdistribution #Weibulldistribution #centrallimittheorem #CLT #FisherTippettGnedenkotheorem #orderstatistics #maximumorderstatistic #minimumorderstatistic #exponentialdistribution #Paretodistribution #MonteCarlosimulation #MonteCarlomethods #Juliaprogramming #Distributions.jl #Juliaeconometrics #simulationbasedmethods #structuraleconometrics #discretechoicemodels #randomutilitymodels #econometricslecture #graduateeconometrics #appliedmicroeconomics #tailbehavior #heavytails #thintails #extremevaluedistributions #limitingdistributions #convergenceindistribution #asymptotictheory #probabilitytheory #economicmodeling #trademodels #EatonKortum #structuraleconguy #economicsPhD #econometricstutorial #econometricsYouTube #VSCodeJulia #Juliaextension #histogramdensityplot