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Mastering Scientific Computing with R by Radia M. Johnson, Paul Gerrard

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Monte Carlo simulations

An important part of statistical analysis is to be able to evaluate expectations of random variables. However, under certain circumstances, it is not feasible to apply a deterministic algorithm or difficult to obtain a closed-form expression. In other words, it is difficult or impossible to express the relationship between the explanatory and response variables under analytical terms using a finite number of elementary functions such as constants, exponents, n roots, and logarithms. A practical way to solve these problems is to use Monte Carlo methods, which are a broad class of computational algorithms that rely on repeated random sampling of quantities to approximate the distribution of an unknown probability distribution. ...

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