I submitted a pull request with an implementation of the Landau distribution, see https://github.com/scipy/scipy/pull/19145. It is not based on the ROOT implementation but on a paper, and the code if you look at it is actually very different, so I hope there are no legal problems. I have been comparing it against the Lévy stable with alpha=beta=1 and found that the Landau implementation is approximately 1500 times faster when calculating the PDF, which actually makes it suitable to fit histograms, and both PDF and CDF seem to be more accurate than the Lévy stable alternative for large values of x, as there are no "discrete jumps" in this region. However, I am not sure about how to test the accuracy in an absolute way, I am just comparing it against the Lévy stable implementation, as you can see in the unittests in my pull request. As a physicist working with radiation detectors, I am in favor of adding it to SciPy. There are mainly two reasons I see: 1) Many colleagues don't seem to know that the Landau is a special case of the Lévy stable distribution (I was one of them for a large fraction of my PhD). If you search for things like "landau distribution python" on the web, you find either implementations that are not in SciPy, or are suggested to use the Moyal distribution, which is not the same. But the Lévy stable distribution appears nowhere in the first page of the search results. As a consequence, many colleagues decide not to use Python simply because they cannot easily find the distribution. This could, in principle, be solved simply by adding some comment to the documentation of the Lévy stable mentioning that the Landau is just a special case of it. 2) After finding out that the Landau is just the Lévy stable with alpha=beta=1, you discover that the calculation of the PDF is so slow that actually it is useless for many applications commonly found in the lab. On top of this, the current implementation of Lévy stable when alpha=beta=1 has a bug in the scale parameter, see https://github.com/scipy/scipy/issues/19140, but let's hope it is solve soon so it should no be a reason in favor of an implementation of the Landau distribution. Please let me know your thoughts on this. Matias.