Measuring poverty is very difficult. First, it is a relative concept and requires the definition of a standard or threshold. Second, as people are usually not normally distributed, any single measure misses some aspect of the distribution. Third, the item whose distribution is measured may not be the appropriate one to represent poverty. Most of the time this is income, but temporary low income is very different from permanent low income, and in both cases, purchasing power may differ dramatically on location, social policies and period. All these difficulties have lead to a plethora of poverty measures. In fact, if you look at the program of any economic inequality conference, there will be plenty of papers on new measures by authors hopeful that their names will stick to a new index or coefficient.
Walter Bossert, Satya Chakravarty and Conchita d'Ambrosio come up with a new measure that emphasizes the persistence of poverty. They are very careful in making their measure following three axioms: the measure corresponds to static poverty in the one period-case, a measure is worse is poverty spells are longer ans spells out of poverty are shorter, and two decomposability axioms too complex to describe here.
The measure they propose is a weighted sum of per period poverty measures, where weight are proportional to the current poverty spell. Using the European Community Household Panel, they find that their measure does not change rankings much whether poverty spell weights are used or not. But I bet they would change quite a bit for the US.