Abstract
The quantitative construction of risk models, risk measurement and analysis are essential to obtain a better appreciation of the risks we confront and to mitigate their effects. To do so, probability theory and statistics are necessary. The purpose of this chapter is to provide a cursory and intuitive introduction to basic elements of probability distributions.
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References and Additional Reading
References and Additional Reading
Additional probability reference sources include both fundamental books, such as Hacking Ian (2006) book on the Emergence of Probability (as well as a series of books on the history and the philosophies of probability), Feller’s 2 volumes (1971), Johnson and Kotz (1969, 1970a) and (1970b) as well as numerous reference books on probability distributions and their properties. In addition, reference books such Abramowitz and Stegun (1965), Gradstein and Ryzhik, (1965) provide an extensive tabulation of some distribution and mathematical functions and integrals which are used to define complex risk probability models, Peizer and Pratt (Part I)as well as Pratt (part II) for normal approximations for binomial, F, Beta and other common, related tail probabilities, Rodriguez (1977) for a guide to the Burr Type XII distributions.
Applications books such as Barlow and Proschan (1965), Bolland and Proschan (1994), and Shaked and Shantikumar (1994) on Reliability, Barrois (1834) on Actuarial statistics, Gerber (19790, on Insurance and Actuarial problems, Kullback (1959) (on Information Statistics and Entropy Functions) are a sample of books in addition to the multitude of references in all professions that are based on elements of probability and their applications.
For example, the following references consulted in various fields, based on the use of probability moments included books and papers by Corrado and Su (1996), Daykin et al. (1994), Denuit (2001), Everitt and Hand (1981), Tadikamalla (1980), Wald and Wolfowitz (1940), Wiggins (1992), Willasen (1981), Yang and Zhang (2000), Brandt and Diebold (2006), on a no arbitrage approach to range based estimation of return covariances and correlations.
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Tapiero, C.S. (2013). Probability Elements: An Applied Refresher. In: Engineering Risk and Finance. International Series in Operations Research & Management Science, vol 188. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6234-7_3
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