Data for measuring poverty are frequently available in a summary form that describes the proportion of income or expenditure for each of a number of population proportions. While various discrete poverty measures can be applied directly to data in this limited form, they typically require an arbitrary approach to within-group interpolation. This problem can be overcome by fitting either a parametric income distribution or a Lorenz curve to the grouped data and computing the required quantities from estimated parameters. The Lorenz curve approach is widely used by the World Bank, but can encounter problems. As an alternative, in this article we show how to calculate several poverty measures from parameters of the generalized beta income distribution, and its popular special cases. An analysis of poverty changes in countries from South and Southeast Asia is used to illustrate the methodology.