## The Monte Carlo method

An alternative method is known as Monte Carlo simulation. It depends on the fact that the histogram of a large random sample approximates the probability function of the underlying random variable.

Suppose that the output variable required to carry out the risk analysis, denoted by Y , is given as a function of a vector X of underlying variables: X = (X1, . . . , Xn) in the form

Y = f (X). (5.1) In the Monte Carlo method, a random sample of size N of the vector of underlying variables X1, . . . , XN is generated. Each such vector is called a realization of the vector X. To each realization there corresponds a value of the output variable Y . Thus we obtain a sample of size N from the output variable Y . Provided N is chosen appropriately large, the histogram of Y will approximate its distribution as closely as required.