The article introduces a new method called topological density estimation (TDE) to better estimate the shape of complex probability distributions. TDE uses the structure of the data to choose the best bandwidth for kernel density estimation, which is a common statistical technique. The researchers found that TDE outperforms other methods in accurately estimating highly complex distributions, saving time and improving performance. TDE can also assess its own suitability for a given dataset and provide additional useful information beyond just density estimation.