How does a Monte Carlo simulation work and what is the influence of the distribution on which the random variable is based

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Hi everyone!

in advance: I am not a native English speaker. Sorry if there are mistakes in my explanations.

I hope, I can get some help understanding the essential processes and dependencies in the field of Monte Carlo simulation.

In the place I work at, the Monte Carlo simulation is used to determine risks. I understood the basic principle of random dice rolling. My main concern is to understand the role of the underlying distribution function. The random variable “economic damage” is based, for example, on a equal distribution or a triangular distribution.

What impact does the assumption of the distribution have? Isn’t there always a normal distribution in a Monte Carlo simulation assumed?

Thanks in advance!

In: 1

**General explanation:**

A Monte Carlo simulation is a way of approximating the probability of certain outcomes by using random variables. In a simple example, if you wanted to know the odds of rolling a six on a six-sided die, you could roll the die many times and count up the number of times you rolled a six. This would give you an estimate of the probability of rolling a six.

In a more complex example, if you wanted to know the odds of something happening over many different trials, you could use a Monte Carlo simulation. For example, if you wanted to know the odds of getting a certain number on 10 rolls of a die, you could set up a simulation in which you would roll the die 10 times and keep track of the number that came up each time. This would give you an estimate of the probability of getting the desired number on 10 rolls.

The role of the underlying distribution is to give you an idea of how likely it is for the random variable to take on different values. For example, if you were using a Monte Carlo simulation to estimate the odds of an event happening, and you were using a distribution that was skewed to the right, this would mean that the event was more likely to happen than if you were using a normal distribution.

**Explanation more specific to your question:**

A Monte Carlo simulation is a technique used to calculate the probability of different outcomes in a situation where you can’t easily calculate the exact answer. It works by randomly selecting a value from a given distribution (i.e. a set of numbers that describe the likelihood of different outcomes), and then doing the calculation you’re interested in a bunch of times, with each time using a different randomly chosen value. By doing this, you can get an idea of how likely different outcomes are, and what the range of possible outcomes might be.

The distribution that the random variable is based on can have a big impact on the results of the simulation. For example, if you’re simulating the outcome of an election, and you’re using a triangular distribution to model the likelihood of different vote totals, your results will be very different than if you use a normal distribution. This is because the triangular distribution is much more peaked than the normal distribution, meaning that there’s a higher chance of getting a very small or very large vote total than there is with a normal distribution.