Poisson Distribution: A Model for Estimating Households by Household Size

Abstract

The number of people living in a household is associated with infrastructure demand such as transportation and water usage. As a result, infrastructure planners often require detail about the number of households by size-of-household at very small levels of geography (census tract or smaller) to calibrate their models. In addition, these data must also be projected into the future in order to support planning efforts. This paper documents a statistical technique for estimating and forecasting the distribution of households by size using a modified application of the Poisson distribution. This technique is valuable to demographers as it provides a simple and reliable tool for estimating the distribution of household sizes at nearly any level of geography for a given point in time using only one input parameter—average household size. There are a wide variety of applications of the Poisson distribution in biology and engineering. However, there are only few documented applications in demography. This article puts forth two key advancements over prior published work: (1) an entirely new, and greatly simplified method for applying the distribution, and (2) evidence of the reliability of the technique for estimating household size distributions in small geographic areas (e.g., counties and census tracts). Tests of the model based on U.S. Census Bureau data for 2010 suggest that the model is suitable for use in estimating the distribution of households by size at the county and census tract level. In addition, practitioners may want to consider adjustments for households of size one and size three, which are consistently under- and over-predicted, respectively.