In the investment world, it’s common to discuss average rates of return. It’s not sufficient, however, to simply add up historical returns and divide by how many there are. The proper way to calculate ...

In many modern sciences, data often exist on curved geometric spaces rather than flat planes, posing challenges for traditional statistical tools. These curved spaces are called Riemannian manifolds.

A. M. Fink and Max Jodeit, Jr. It is shown that the arithmetic mean of $x_1 w_1,\ldots, x_n w_n$ exceeds the geometric mean of $x_1,\ldots, x_n$ unless all the $x$'s ...