A Numerical Approximation of the Median of the Gamma Distribution using Newton’s Method

Abstract

The Gamma Distribution is widely used in various real-world applications. However, directly finding its median can be challenging due to the lack of a simple closed-form expression. In this project, we will use Newton’s Method, an iterative algorithm for finding zeros of functions. By applying this method, we can approximate the median efficiently and with greater precision than former methods. Our implementation in Python also allows for increased applicability as we expand the approximation of the median for distributions where the rate parameter is not 1.