# Inverse Transform Sampling Inverse transform sampling to generate random samples from a distribution given its cumulative distribution function (CDF). > The core idea is to leverage the uniform distribution, which is simple to sample from, to generate samples from more complex distributions. ### How does it work? 1. **Uniform Distribution as a Starting Point** Begin with samples from a uniform distribution over the interval $[0,1]$. These can be easily generated using standard random number generators. 1. **Cumulative Distribution Function (CDF)** Identify the CDF of the target distribution from which you want to sample. The CDF, $F(x)$, is a function that maps a value $x$ to the probability that a random variable drawn from the distribution is less than or equal to $x$. 1. **Inverse Transformation** Apply the inverse of the CDF, $F^{-1}(u)$, to each uniform random sample $u$. The function $F^{-1}$ is known as the quantile function. 1. **Sampling from Desired Distribution** The result of this transformation, $F^{-1}(u)$, gives a sample that follows the desired distribution. --- Date: 20231206 Links to: Tags: References: * []()