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Random Variables

Michele Leonardo Bianchi, Stoyan V Stoyanov, Gian Luca Tassinari, Frank Fabozzi () and Sergio M Focardi

Chapter 2 in Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management, 2019, pp 23-70 from World Scientific Publishing Co. Pte. Ltd.

Abstract: After formally introducing the notion of random variable and some related concepts, in this chapter we look at discrete and absolutely continuous random variables. We focus our attention on definitions and properties that will be needed in the chapters that follow. The main topics covered in this chapter are:basic definitions of probability theory;the definition of the characteristic function and other generating functions, and their main properties for real-valued random variables;a review of some univariate discrete random variables (Bernoulli, binomial and Poisson);a review of some univariate continuous random variables (gamma, exponential, inverse Gaussian, normal, log-normal, variance gamma, normal inverse Gaussian);a review of the multivariate normal distribution.

Keywords: Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2019
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