Generating Continuous Random Variables

Simulating Uniform Distribution

• using pseudo-random numbers or specialized tables

Inverse Transform Method
Smirnov Transform

• simple method of generating continuous random variables of a particular continuous distribution
• generate uniform random numbers and plug them into the inverse function of the continuous distribution’s CDF
• however, computing inverse function is expensive, and may not always exist

Gaussian Inverse CDF

• TODO

Sampling

• when Inverse Transform Method is too hard. In other words, cumulative distribution function 𝐹(𝑥) has a complicated form but a probability density function 𝑓(𝑥) is available, random variables with this density can be generated by Rejection Method

Box Muller

• method for simulating a normal distribution