Probability distribution functions (PDFs) describe the expected values of random variables drawn from a sample. The shape of the PDF explains how likely it is that an observed value might occur.

When do probability distribution functions (PDFs) about future climate misrepresent uncertainty? How can we recognise when such misrepresentation occurs and thus avoid it in reasoning about or ...

Let Bn = Sn (Sn + αn TN)⁻¹, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we ...