ABSTRACT
This chapter explores about the mathematical sociology and human rights. The tools of mathematical sociology can be used to build rich theories with abundant testable predictions. The clarity and transparency of mathematical sociology makes it an ideal way to describe and assess basic issues of human rights. It begins with three widely used continuous univariate distributions: the lognormal, Pareto, and power-function. It also includes the study of distributive/retributive justice, in which there are three matrices, corresponding to the three quantities in the justice-evaluation function: the actual reward, the just reward, and the justice evaluation. The goal of scientific work is to understand more fundamental social-science theories that are capable of predicting the justice-evaluation function and the status function. If the function has a special sociological meaning, and if substantial further searches fail to find a probability distribution with a quantile function, then it means a new probability distribution.
