Abstract
This chapter presents a discussion on probability distributions. The chapter begins with the basic notions of mathematical statistics that form the framework for analysis of financial data. The chapter lists a number of distributions that are widely used in statistical data analysis such as the uniform distribution, binomial distribution, normal (or Gaussian) distribution, Poisson distribution, lognormal distribution, Cauchy distribution, Gumbel distribution, Frechet distribution, Pareto distribution, and Weibull distribution. The stable distributions, also known as the “Levy distributions,” that have become popular in econophysics research are discussed. The chapter concludes with a discussion on scale invariance.
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