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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Aitchison, J. (1955). On the distribution of a positive random variable having a discrete probability mass at the origin. Journal of the American Statistical Association,50(271), 901–908.
Arbués, F., Villanúa, I., & Barberán, R. (2010). Household size and residential water demand: An empirical approach. The Australian Journal of Agricultural and Resource Economics,54(1), 61–80. https://doi.org/10.1111/j.1467-8489.2009.00479.x.
Beaghen, M., & Stern S. (2009). Usability of the American Community Survey Estimates of the Group Quarters Population for Sub-state Geographies. In: Presentation for the joint statistical meeting of the American Statistical Association, Washington, DC.
Jarosz, B. (2010). Household size in the American Community Survey. In: Presentation for the MPO/COG mini-conference on socio-economic modeling, San Diego, CA.
Jennings, V., & Lloyd-Smith, B. (1992). Household change, distribution of household size, and fertility rates. In: Presentation for the Australian Population Association Conference, Sydney.
Jennings, V., Lloyd-Smith, B., & Ironmonger, D. (1999). Household size and the Poisson distribution. Journal of the Australian Population Association. https://doi.org/10.1007/BF03029455.
Johnson, L., Norman, A., Kemp, W., & Kotz, S. (2005). Univariate discrete distributions (3rd ed.). Hoboken: Wiley.
Marton, K., & Voss, P. (2010). Measuring the group quarters population in the american community survey: Interim report. Washington: The National Academies Press.
Motulsky, H. (2010). Intuitive biostatistics (2nd ed.). New York: Oxford University Press.
National Research Council. (2007). Using the American Community Survey: Benefits and Challenges. Washington, DC: The National Academies Press. https://doi.org/10.17226/11901.
Ruggles, S., Fitch, C., Magnuson, D., & Schroeder, J. (2019) Differential privacy and census data: Implications for social and economic research. In: AEA papers and proceedings (Vol. 109).
SANDAG. (2015). CONCEP 2015, San Diego, CA. Retrieved Nov 18, 2019 from https://github.com/SANDAG/CONCEP/blob/master/docs/concep4.0%20-%202015.docx.
San Diego Association of Governments (SANDAG). (2011). CONCEP Model Documentation, San Diego, CA.
U.S. Census Bureau. (2015). United States Public Use Microdata Sample (PUMS): 2010 Census of Population and Housing, Technical Documentation. Retrieved Nov 18, 2019 from https://www2.census.gov/programs-surveys/decennial/2010/technical-documentation/complete-tech-docs/us-pums/pumsus.pdf?#.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Jarosz, B. Poisson Distribution: A Model for Estimating Households by Household Size. Popul Res Policy Rev (2020). https://doi.org/10.1007/s11113-020-09575-x
- Household size
- Poisson distribution
- Census tract
- Comparison of model and survey
- Estimation method