Overview
Simulations are a way to approximately compute the statistics areound a give process or distribution when you dont know how to derive an analytical formula for that statistic.For example, lets say you wanted to know what the standard deviation of a coin flip was. If you didnt know the formula, but you did have a program that generated 0s and 1s with a 50% probability each, you could just generate a large number of 0s and 1s and take the standard deviation. This number would be approximately the true standard deviation of the distribution itself.
Topics
- Simulating a Uniform Distribution
- Simulating Other Distributions
- Plotting Simulated Distributions
- Simulating Multi Variable Distributions : many problems involve more than one variable. In these cases, we need a method to generate variables from a given multivariable distribution. If the variables are independent, then we can get generate them separately. However, independent variables are rare.
- Simulating Time Series - time series are unique in that the data is ordered sequentially, and on item in the series is (typically) dependent on other items in the sequence, usually the items close to it in the ordering.
- Solving Integration Problems with Monte Carlo