Anna Sączewska-Piotrowska

(Polish) PDF


The article analyses households’ poverty and nonpoverty duration. For this purpose survival function estimators for recurrent events were used: Wang-Chang estimator and two estimators proposed by Pena, Strawderman and Hollander (IIDPLE and FRMLE). We can conclude that survival probability for a long time out of poverty is greater than in the case of survival in poverty. Based on the graphical method we can conclude that the best estimator of survival in poverty and out of poverty is FRMLE. It means that we cannot assume that interoccurrence times within households are independent and identically distributed.


poverty, survival function, recurrent events, nonparametric estimation


Allison P. D., (2010), Survival Analysis, w: Hancock G. R., Mueller R. O., (red.), The Reviewer’s Guide to Quantitative Methods in the Social Sciences, Routlege, New York, 423–424.

Andriopoulou E., Tsakloglou P., (2011), The Determinants of Poverty Transitions in Europe and the Role of Duration Dependence, IZA Discussion Paper No. 5692, Bonn, Germany.

Atkinson T., Cantillon B., Marlier E., Nolan B., (2002), Social Indicators. The EU and Social Inclusion, Oxford University Press, New York.

Bane M. J., Ellwood D. T., (1986), Slipping Into and Out of Poverty: The Dynamics of Spells, The Journal of Human Resources, 21 (1), 1–23.

Bieszk-Stolorz B., Markowicz I., (2012), Modele regresji Coxa w analizie bezrobocia, CeDeWu, Warszawa.

Breslow N., Crowley J., (1974), A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship, Annals of Statistics, 2 (3), 437–453.

Callens M., Croux C., (2009), Poverty Dynamics in Europe. A Multilevel Discrete-Time Recurrent Hazard Analysis, International Sociology, 24 (3), 368–396.

Collett D., (2003), Modelling Survival Data in Medical Research, Chapman and Hall/CRC, Boca Raton, Florida.

Fouarge D., Layte R., (2005), Welfare Regimes and Poverty Dynamics: The Duration and Recurrence of Poverty Spells in Europe, Journal of Social Policy, 34 (3), 407–426.

Frątczak E., Gach-Ciepiela U., Babiker H., (2005), Analiza historii zdarzeń. Elementy teorii, wybrane przykłady zastosowań, SGH, Warszawa.

González J. R., (2006), Inference for a General Class of Models for Recurrent Events with Application to Cancer Data, Universitat Politecnica de Catalunya, Barcelona, praca doktorska.

González J. R., Pena E. A., (2003), Bootstrapping Median Survival with Recurrent Event Data, IX Conferencia Espanola de Biometría, A Coruna, 2003 May 28–30.

González J. R., Pena E. A., (2004), Estimación no Paramétrica de la Función de Supervivencia Para Datos con Eventos Recurrentes, Revista Espanola de Salud Pública, 78 (2), 189–199.

González J. R., Pena E. A., Strawderman R. L., (2015), Survrec: A Package for Survival Analysis for Recurrent Event Data, URL

Greenwood M., (1926), The Natural Duration of Cancer, Reports of Public Health and Related Subjects, Volume 33, Her Majesty’s Stationery Offi ce, London, 1–26.

Gutiérrez E., Lozano S., González J. R., (2011), A Recurrent-Events Survival Analysis of the Duration of Olympic Records, IMA Journal of Management Mathematics, 22 (2), 115–128.

Hagenaars A. J. M., de Vos K., (1988), The Defi nition and Measurement of Poverty, The Journal of Human Resources, 23 (2), 211–221.

Hagenaars A. J. M., van Praag B. M. S., (1985), A Synthesis of Poverty Line Defi nitions, Journal of the International Association for Research in Income and Wealth, 31 (2), 139–154.

Hollifi eld E., Trevino V., Zarn A., (2012), A Survival Analysis of the Duration of Olympic Records, arXiv:1207.6133 [stat.AP].

Hosmer D. W., Lemeshow S., May S., (2008), Applied Survival Analysis. Regression Modeling of Timeto-Event Data, John Wiley & Sons, Inc., Hoboken, New Jersey.

Kaplan E. L., Meier P., (1958), Nonparametric Estimation From Incomplete Observations, Journal of the American Statistical Association, 53 (282), 457–481.

Kelly P. J., Lim L. L.-Y., (2000), Survival Analysis for Recurrent Event Data: An Application to Childhood Infectious Diseases, Statistics in Medicine, 19 (1), 13–33.

Kleinbaum D. G., Klein M., (2005), Survival Analysis. A Self-Learning Text, Springer, New York.

Layte R., Fouarge D., (2004), The Dynamics of Income Poverty, w: Berthoud R., Iacovou M., (red.), Social Europe: Living Standards and Welfare States, Edward Elgar, Cheltenham, 202–224.

Mills M., (2011), Introducing Survival and Event History Analysis, SAGE Publications, Los Angeles-London-New Dehli-Singapore-Washington DC.

Panek T., (2011), Ubóstwo, wykluczenie społeczne i nierówności. Teoria i praktyka pomiaru, SGH, Warszawa.

Panek T., Podgórski J., Szulc A., (1999), Ubóstwo: teoria i praktyka pomiaru, Monografi e i Opracowania 453, SGH, Warszawa.

Pena E. A., Strawderman R. L., Hollander M., (2001), Nonparametric Estimation with Recurrent Data, Journal of the American Statistical Association, 96 (456), 1299–1315.

Peterson A. V., (1977), Expressing the Kaplan-Meier Estimator as a Function of Empirical Subsurvival Function, Journal of the American Statistical Association, 72 (360), 854–858.

Rada Monitoringu Społecznego, (2013), Diagnoza społeczna 2000–2013: zintegrowana baza danych, [29 października 2014 r.].

R Development Core Team, (2015), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, URL

Rodgers J. R., Rodgers J. L., (1993), Chronic Poverty in the United States, The Journal of Human Resources, 28 (1), 25–54.

Stevens A. H., (1994), The Dynamics of Poverty Spells: Updating Bane and Ellwood, American Economic Review, 84 (2), 34–37.

Stevens A. H., (1999), Climbing Out of Poverty, Falling Back in. Measuring the Persistence of Poverty Over Multiple Spells, The Journal of Human Resources, 34 (3), 557–588.

Therneau T. M., Lumley T., (2015), Survival: A Package for Survival Analysis in S, R Package Version 2.37-7, URL

Topińska I., (2008), Kierunki zmian w statystyce ubóstwa, w: Topińska I., (red.), J. Ciecieląg, A. Szukiełojć-Bieńkuńska, Pomiar ubóstwa. Zmiany koncepcji i ich znaczenie, IPiSS, Warszawa, 8–26.

Wang M.-C., Chang S.-H., (1999), Nonparametric Estimation of a Recurrent Survival Function, Journal of the American Statistical Association, 94 (445), 146–153.

Back to top
© 2019–2022 Copyright by Statistics Poland, some rights reserved. Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) Creative Commons — Attribution-ShareAlike 4.0 International — CC BY-SA 4.0