The analysis and measurement of poverty is a crucial issue in the field of social science. Poverty is a multidimensional notion that can be measured using composite indicators relevant to synthesizing statistical indicators. Subjective choices could, however, affect these indicators. We propose interval-based composite indicators to avoid the problem, enabling us in this context to obtain robust and reliable measures. Based on a relevant conceptual model of poverty we have identified, we will consider all the various factors identified. Then, considering a different random configuration of the various factors, we will compute a different composite indicator. We can obtain a different interval for each region based on the distinct factor choices on the different assumptions for constructing the composite indicator. So we will create an interval-based composite indicator based on the results obtained by the Monte-Carlo simulation of all the different assumptions. The different intervals can be compared, and various rankings for poverty can be obtained. For their parameters, such as center, minimum, maximum, and range, the poverty interval composite indicator can be considered and compared. The results demonstrate a relevant and consistent measurement of the indicator and the shadow sector's relevant impact on the final measures.