How should Engel's law be formulated?

Engel's law expresses a “negative stochastic association” of income and the proportion of income that is spent on food. However, there are many quite different notions of “negative stochastic association” and consequently there are different ways of defining Engel's law. We relate these different concepts to Engel's original statistical analysis and show that one must give credit to Engel for the first non-parametric statistical analysis of budget-data.