An adequate stochastic model for shares as dependent variables is provided by the Dirichlet distribution. The paper considers two different parametrizations which lead to linear and nonlinear Dirichlet share equations. Using an inequality for the trigamma function the global concavity of the...

Share equations play an important role in applied economic research, notably in marketing and demand analysis. Both market shares and budget shares have been used as dependent variables in econometric models which were partly motivated by microeconomic theory. However attempts of econometricians...

In this study, we utilize an input-output (I-O) model to perform an ex-post analysis of the COVID-19 pandemic workforce disruptions in the Philippines. Unlike most disasters that debilitate physical infrastructure systems, the impact of disease pandemics like COVID-19 is mostly concentrated on...

Chotikapanich and Griffiths (2002) introduced the Dirichlet distribution to the estimation of Lorenz curves. This distribution naturally accommodates the proportional nature of income share data and the dependence structure between the shares. Chotikapanich and Griffiths (2002) fit a family of...

Do the rich always get richer by investing in a cryptocurrency for which new coins are issued according to a Proof-of-Stake (PoS) protocol? We answer this question in the negative: Without trading, the investor shares in the cryptocurrency are martingales that converge to a well-defined limiting...