This paper attempts to provide a synthetic view of varied techniques available for per- forming inference on income distributions. Two main approaches can be distinguished: one in which the object of interest is some index of income inequality or poverty, the other based on notions of stochastic dominance. From the statistical point of view, many techniques are common to both approaches, although of course some are specific to one of them. I assume throughout that inference about population quantities is to be based on a sample or samples, and, formally, all randomness is due to that of the sampling process. Inference can be either asymptotic or bootstrap-based. In principle, the bootstrap is an ideal tool, since in this paper I ignore issues of complex sampling schemes, and suppose that observations are IID. However both bootstrap inference, and, to a considerably greater extent, asymptotic inference can fall foul of difficulties associated with the heavy right-hand tails observed with many income distributions. I mention some recent attempts to circumvent these difficulties.
