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- W2482312156 abstract "This chapter discusses a central concept for applying Monte Carlo methods, namely random generation. C++ classes that model pseudo random number generators, distributions, and mechanisms to combine them to create working C++ code are developed. The mechanism to generate uniform random numbers and then, another mechanism to transform a uniform random number into one from a given distribution are described. The chapter reviews Ran2 as a congruential generator and the Mersenne Twister algorithm as a representative of a shift register random number generator. The Sobol sequence from the class of quasi random generators is discussed and the C++ code is presented. To illustrate the mechanism of transforming uniform random numbers into those of a given distribution, the inversion method and the acceptance/rejection method are reviewed. The chapter discusses Poisson distribution, which gives an account of Poisson processes and processes that are based on simple Poisson processes. The process of using such processes to simulate jump diffusion processes is used. Such process are used in quantitative finance to model fat tails of terminal distributions as well as unpredictable and rare events occurring in the credit market." @default.
- W2482312156 created "2016-08-23" @default.
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- W2482312156 date "2012-01-02" @default.
- W2482312156 modified "2023-09-25" @default.
- W2482312156 title "Random Number Generation and Distributions" @default.
- W2482312156 doi "https://doi.org/10.1002/9780470685167.ch22" @default.
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