1 citations · 1 across the 7 of their papers we have counts for
8 papers
The Power Problem for Generalized Gamma Convolutions (GGC) and Related Questions
Tord Sjödin
The class of generalized gamma convolutions (GGC) is closed with respect to (wrt) change of scales, weak limits and addition and multiplication of independent random variables. Our…
On Mixtures of Gamma Distributions, Distributions with Hyperbolically Monotone Densities and Generalized Gamma Convolutions (GGC)
Tord Sjödin
Let be a standard Gamma(k) distributed random variable, , and let be an independent positive random variable. We prove that if has a hyperbolically monotone densit…
A Short and Unified Proof of Kummer's Test
Tord Sjödin
Kummer's test from 1835 states that the positive series is convergent if and only if there is a sequence of positive numbers such that $…
Archimedian Theorems for Composite Solids
Tord Sjödin
We consider the Center of Gravity of a solid, partly filled with some homogeneous material, and find its qualitative and quantitative properties. In particular, we prove that the C…
On Multivariate Hyperbolically Completely Monotone Densities and Their Laplace Transforms
Tord Sjödin
The class HCM consists of all nonnegative functions f such that f(uv)*f(u/v)is completely monotone with respect to w=v+1/v, for all fixed positive numbers u, and has been extensive…
A short proof of the Fundamental Theorem of Algebra
Tord Sjödin
D'Alembert made the first serious attempt to prove the Fundamental Theorem of Algebra (FTA) in 1746. An elementary proof of (FTA) based on the same idea is given in Proofs from THE…
A short proof of d'Alemberts theorem
Tord Sjödin
A classical theorem of d'Alembert states that if a polynomial P(x) with real coefficients has a non-real root x=a+ib, then it also has a root x=a-ib. We give a short and elementary…
A Note on Gram-Schmidt's Algorithm for a General Angle
Tord Sjödin
The Gram-Schmidt algorithm produces a pairwise orthogonal set from a linearly independent set of vectors in an inner product vector space V. We give a linear algorithm that constru…