One of the methods to estimate the poverty level inside a given population is based on how to define the poverty line values. Each person having his income under the poverty threshold will be considered to be poor. In the literature we distinguish at least three approaches: to evaluate the absolute poverty line, to find a relative poverty threshold depending on the main indicators of the income distribution in the analyzed community or to assume a subjective point of view. The procedures for determining the relative poverty lines are based in practice on the mean or the median of the population income. To assure a concordance between the concrete estimation of several possible poverty thresholds and the poverty and inequality real phenomena we proposed to be verified three conditions. Finally, we also proved by examples that each of these restrictions are not obligatory satisfied by an arbitrary real positive data set. The present study will be extended in the future to assure a theoretical support for estimating more exactly the relative poverty lines.