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When to use Monte Carlo simulation to approximate a distribution?
Monte Carlo simulation is a powerful tool for approximating a distribution when deriving the exact one is difficult. This situation can arise when a complicated transformation is applied to a random variable (RV), of which we know its distribution.
How is the probability of a discrete RV calculated?
The probability of any given value occurring is zero, so you must integrate over a range of values to find the probability that the RV falls within the specified range. For discrete RVs, this function is called a probability mass function (PMF) and it returns the probability of a specific value occurring.
How to simulate a stochastic model of population growth?
I’m trying to simulate a stochastic model of deterministic exponential population growth, where d N / d t = r N where N is population size and r is rate ( t time). I’m assuming there’s no carrying capacity. This page ( http://cnr.lwlss.net/DiscreteStochasticLogistic/) suggests this algorithm for simulating growth on an interval [ 0, t e n d]:
Why are the results of a simulation so erratic?
The whole point of simulation is to show you that such variation is realistic. In fact, there appears to be nothing wrong with your results–except that you haven’t yet done enough simulations to appreciate what they are telling you. In this case, the results are especially erratic because the starting population is so small.
Why do we use random sampling in Monte Carlo?
This may be due to many reasons, such as the stochastic nature of the domain or an exponential number of random variables. Instead, a desired quantity can be approximated by using random sampling, referred to as Monte Carlo methods.
When do you use a Monte Carlo method?
Monte Carlo methods are a class of techniques for randomly sampling a probability distribution. There are many problem domains where describing or estimating the probability distribution is relatively straightforward, but calculating a desired quantity is intractable.
How is a Monte Carlo forecast different from a normal forecast?
Unlike a normal forecasting model, Monte Carlo Simulation predicts a set of outcomes based on an estimated range of values versus a set of fixed input values.