Integração por aproximação: simulação via Monte Carlo.

Abstract

In this work, we showed one statistical method that is the simulation by the Monte Carlo Method. Initially, we used an explanation about integrals and polar coordinates, useful tool in the determination of integral of a function known, which is important in various areas of applications. Then, we studied continuous random variables with any probability distributions, which are simulated from numbers uniformly distributed within a certain range by certain transformations. The Monte Carlo method is a mechanism that generates data from a simulator of random numbers and distributions of frequencies of interest which features the stochastic processes considered by the simulation model. We based on these features of the method, we solved approximates integrals through Monte Carlo simulation, using the language R. We solved analytically integrals of different degrees of complexity, obtaining your absolute result of analytical and numerical mode.Then, we compared with the result via Monte Carlo simulation with the absolute results, obtaining similar results according with the incresead number of simulated values.