Monte Carlo method or Monte Carlo analysis

The Monte Carlo method, also called Monte Carlo analysis, is a means of statistical evaluation of mathematical function s using random samples. This requires a good source of random numbers . There is always some error involved with this scheme, but the larger the number of random samples taken, the more accurate the result.

In its pure mathematical form, the Monte Carlo method consists of finding the definite integral of a function by choosing a large number of independent-variable samples at random from within an interval or region, averaging the resulting dependent-variable values, and then dividing by the span of the interval or the size of the region over which the random samples were chosen. This differs from the classical method of approximating a definite integral, in which independent-variable samples are selected at equally-spaced points within an interval or region.

The Monte Carlo method is most famous for its use during the Second World War in the design of the atomic bomb. It has also been used in diverse applications, such as the analysis of traffic flow on superhighways, the development of models for the evolution of stars, and attempts to predict fluctuations in the stock market. The scheme also finds applications in integrated circuit ( IC ) design, quantum mechanics , and communications engineering.

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