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Trends in disguise

Published online by Cambridge University Press:  16 September 2014

Vytaras Brazauskas*
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201, U.S.A
Bruce L. Jones
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada
Ričardas Zitikis
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada
*
*Correspondence to: Vytaras Brazauskas, Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA. Tel: 414-229-5656; Fax: 414-229-4907; E-mail: vytaras@uwm.edu

Abstract

Human longevity is changing, but at what rate? Insurance claims are increasing, but at what rate? Are the trends that we glean from data true or illusionary? The shocking fact is that true trends might be quite different from those that we actually see from visualised data. Indeed, in some situations the upward trends (e.g. inflation) may even look decreasing (e.g. deflation). In this paper, we discuss this “trends in disguise” phenomenon in detail and offer a way for estimating true trends.

Type
Papers
Copyright
© Institute and Faculty of Actuaries 2014 

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References

Bebbington, M., Lai, C.D., Murthy, D.N.P. & Zitikis, R. (2011a). Rational polynomial hazard functions. International Journal of Performability Engineering, 6, 3552.Google Scholar
Bebbington, M., Lai, C.D. & Zitikis, R. (2011b). Modelling deceleration in senescent mortality. Mathematical Population Studies, 18, 1837.CrossRefGoogle Scholar
Brazauskas, V., Jones, B.L. & Zitikis, R. (2009). When inflation causes no increase in claim amounts. Journal of Probability and Statistics, 2009, 110.Google Scholar
Brazauskas, V. & Kleefeld, A. (2011). Folded- and log-folded-t distributions as models for insurance loss data. Scandinavian Actuarial Journal, 2011(1), 5974.Google Scholar
Brazauskas, V. & Kleefeld, A. (2014). Authors’ reply to “Letter to the Editor: Regarding folded models and the paper by Brazauskas and Kleefeld (2011)” by Scollnik. Scandinavian Actuarial Journal, 2014(8), 753757.Google Scholar
Brickmann, S., Forster, W. & Sheaf, S. (2005). Claims inflation – uses and abuses, GIRO Convention 2005, October 18–21, 2005. Blackpool, England.Google Scholar
Cavallo, A., Rosenthal, B., Wang, X. & Yan, J. (2012). Treatment of the data collection threshold in operational risk: a case study with the lognormal distribution. Journal of Operational Risk, 7(1), 338.CrossRefGoogle Scholar
Committee on Post-Employment Benefit Plans (2012). Health care trend rate. Educational Note, May 2012, Canadian Institute of Actuaries, Ottawa, Canada.Google Scholar
Ediev, D.M. (2011). Life expectancy in developed countries is higher than conventionally estimated. Implications from improved measurement of human longevity. Journal of Population Ageing, 4, 532.Google Scholar
Ediev, D.M. (2013). Decompression of period old-age mortality: when adjusted for bias, the variance in the ages at death shows compression. Mathematical Population Studies, 20, 137154.Google Scholar
Fackler, M. (2011). Inflation and excess insurance, ASTIN Colloquium 2011, Parallel Session 8, June 19–22, 2011, Madrid, Spain.Google Scholar
Gesmann, M., Rayees, R. & Clapham, E. (2013). A known unknown, The Actuary, 2 May. Available at http://www.theactuary.com/features/2013/05/a-known-unknown/.Google Scholar
Green, R.M. & Bebbington, M.S. (2013). A longitudinal analysis of infant and senescent mortality using mixture models. Journal of Applied Statistics, 40(9), 19071920.Google Scholar
Klugman, S.A., Panjer, H.H. & Willmot, G.E. (2008). Loss Models: From Data to Decisions, 3rd edition. Wiley, New York, NY.Google Scholar
Lai, C.D. & Xie, M. (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York, NY.Google Scholar
Li, Z. & Sendova, K.P. (2014). On a ruin model with both interclaim times and premiums depending on claim sizes. Scandinavian Actuarial Journal, 2013, http://dx.doi.org/10.1080/03461238.2013.811096.Google Scholar
Marshall, A.W. & Olkin, I. (2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families. Springer, New York, NY.Google Scholar
Opdyke, J.D. & Cavallo, A. (2012). Estimating operational risk capital: the challenges of truncation, the hazards of MLE, and the promise of robust statistics. Journal of Operational Risk, 7(3), 390.Google Scholar
Scollnik, D.P.M. (2014). Letter to the Editor: regarding folded models and the paper by Brazauskas and Kleefeld (2011). Scandinavian Actuarial Journal, 2014(3), 278281.Google Scholar
Sendova, K.P. & Zitikis, R. (2012). The order-statistic claim process with dependent claim frequencies and severities. Journal of Statistical Theory and Practice, 6(4), 597620.Google Scholar