Skip to main content
SpringerLink
Log in

Bayesian semiparametric quantile regression modeling for estimating earthquake fatality risk

  • Published:
Empirical Economics Aims and scope Submit manuscript

Abstract

This paper develops a Bayesian semiparametric quantile regression model for count data. The count responses are converted to continuous responses through the “jittered” method and a transform function. A Bayesian semiparametric quantile regression modeling approach is then developed. The error distribution in the quantile regression model is assumed to be a mixture of asymmetric Laplace distributions constructed with Dirichlet process. Historical death tolls of China caused by earthquakes from 1969 to 2006 are used for fitting, and a parametric model is employed for model comparison. The results of model comparison show that the proposed semiparametric quantile regression model outperforms the parametric model. The empirical analysis illustrates that the impact of earthquake magnitude on death tolls is significant. Moreover, the impact of the magnitude is more pronounced on higher percentiles of death tolls.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Badal J, Vázquez-Prada M, González A (2005) Priliminary quantitative assessment of earthquake casualties. Nat Hazards 34:353–374

    Article  Google Scholar 

  • Bali T (2003) The generalized extreme value distribution. Econ Lett 79:423–427

    Article  Google Scholar 

  • Balkema A, de Haan L (1974) Residual life time at great age. Ann Prob 2:792–804

    Article  Google Scholar 

  • Beckett S, Jee J, Ncube T, Pompilus S, Washinton Q, Singh A, Pal N (2014) Zero-inflated poisson (zip) distribution: parameter estimation and applications to model data from natural calamities. J Risk Insur 6:751–767

    Google Scholar 

  • Bernardi M, Gayraud G, Petrella L (2015) Bayesian tail risk interdependence using quantile regression. Bayesian Anal 10(3):553–603

    Article  Google Scholar 

  • Bohning D (1998) Zero-inflated poisson models and CA man: a tutorial collection of evidence. Biomet J 40:833–843

    Article  Google Scholar 

  • Boucher J, Denuit M, Guillen M (2009) Number of accidents or number of claims? An approach with zero-inflated poisson models for panel data. J Risk Insur 76(4):821–846

    Article  Google Scholar 

  • Chernozhukov V, Hansen C (2006) Instrumental quantile regression inference for structural and treatment effect models. J Econom 132(2):491–525

    Article  Google Scholar 

  • Cheung Y (2002) Zero-inflated models for regression analysis of count data: a study of growth and development. Stat Med 21:1461–1469

    Article  Google Scholar 

  • Coles S (2001) An introduction to statistical modeling of extreme values. Springer, New York

    Book  Google Scholar 

  • Czajkowski J, K S, D S (2011) An analysis of coastal and inland fatalities in landfalling US hurricanes. Nat Hazards 59:1513–1531

    Article  Google Scholar 

  • Fernandes W, NaghettiniM Loschi R (2010) A Bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions. Stoch Environ Res Risk Assess 24(8):1127–1143

    Article  Google Scholar 

  • Fuzi MFM, Jemain AA, Noriszura I (2016) Bayesian quantile regression model for calim count data. Insur Math Econ 66:124–137

    Article  Google Scholar 

  • Gelfand A, Kottas A, MacEachern S (2005) Bayesian nonparametric spatial modeling with Dirichlet process mixing. J Am Stat Assoc 100(471):1021–1035

    Article  Google Scholar 

  • Gutiérrez E, Taucer F, Groeve T, Al-Khudhairy D, Zaldivar J (2005) Analysis of worldwide earthquake mortality using multivariate demographic and seismic data. Am J Epidemiol 161:1151–1158

    Article  Google Scholar 

  • Ibrahim J, Chen M, Sinha D (2001) Criterion-based methods for Bayesian model assessment. Stat Sin 11:419–443

    Google Scholar 

  • Ishwaran H, Zarepour M (2002) Dirichlet prior sieves in finite normal mixtures. Stat Sin 12:941–963

    Google Scholar 

  • Karlis D, Ntzoufras I (2003) Analysis of sports data using bivariate Poisson models. J R Stat Soc D 52:381–393

    Article  Google Scholar 

  • Karlis D, Ntzoufras I (2006) Bayesian analysis of the differences of count data. Stat Med 25:1885–1905

    Article  Google Scholar 

  • Koenker R (2005) Quantile regression. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Koenker R, Bassett G (1978) Regression quantiles. Insur Econom 46:33–50

    Google Scholar 

  • Koenker R, Zhao Q (1996) Conditional quantile estimation and inference for arch models. Econom Theory 12:793–813

    Article  Google Scholar 

  • Kottas A, Krnjajić (2009) Bayesian semiparametric modelling in quantile regression. Scand J Stat 36:297–319

    Article  Google Scholar 

  • Lee M (1992) Median regression for ordered discrete response. J Econom 51:59–77

    Article  Google Scholar 

  • Lee D, Neocleous T (2010) Bayesian quantile regression for count data with application to environmental epidemiology. J R Stat Soc Ser C 59(5):905–920

    Article  Google Scholar 

  • Li L, Wang J, Leung H, Zhao S (2012a) A Bayesian method to mine spatial data sets to evaluate the vulnerability of human beings to catastrophic risk. Risk Anal 32(6):1072–92

    Article  Google Scholar 

  • Li Y, Yutaka K, Pan J, Song X (2012b) A criterion-based model comparison statistic for structural equation models with heterogeneous data. J Multivar Anal 112:92–107

    Article  Google Scholar 

  • Li Y, Tang N, Jiang X (2016) Bayesian approaches for analyzing earthquake catastrophic risk. Insur Math Econ 68:110–119

    Article  Google Scholar 

  • Machado J, Silva J (2005) Quantiles for counts. J Am Stat Assoc 100(472):1226–1237

    Article  Google Scholar 

  • Pickands J (1975) Statistical inference using extreme order statistics. Ann Stat 3:119–131

    Article  Google Scholar 

  • Pitt D (2006) Regression quantile analysis of claim termination rates for income protection insurance. Ann Actuar Sci 1(II):345–357

    Article  Google Scholar 

  • Powell J (1984) Least absolute deviation estimation for the censored regression model. J Econom 25:303–325

    Article  Google Scholar 

  • Powell J (1986) Censored regression quantiles. J Econom 32:143–155

    Article  Google Scholar 

  • Sethuraman J (1994) A constructive definition of Dirichlet priors. Stat Sin 4:639–650

    Google Scholar 

  • Smith RL (2003) Statistics of extremes with applications in environment, insurance and finance. University of North Carolina, Chapel Hill

    Book  Google Scholar 

  • Turkan S, Özel G (2014) Modelling destructive earthquake casualties based on a comparative study for Turkey. Nat Hazards 72:1093–1110

    Article  Google Scholar 

  • Yip K, Yau K (2005) On modeling claim frequency data in general insurance with extra zeros. Insur Math Econom 36(2):153–163

    Article  Google Scholar 

  • Yu K, Moyeed R (2001) Bayesian quantile regression. Stat Probab Lett 54:437–447

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Southern University of Science and Technology of China, Shenzhen, Guangdong, China

    Xuejun Jiang

  2. Department of Insurance, Yunnan University of Finance and Economics, Kunming, China

    Yunxian Li & Ruowei Zhou

  3. College of Economics and Management, Nanjing Forestry University, Nanjing, Jiangsu, China

    Aijun Yang

Authors
  1. Xuejun Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yunxian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aijun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ruowei Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunxian Li.

Additional information

The authors are grateful to the editor and the reviewers for their valuable comments and suggestions. This research is supported by National Social Science Fund of China No. 13CTJ002 and No. 16ZDA052, National Natural Science Fund of China No. 11501294 and No. 11871263, Natural Science Foundation of Guangdong Province of China No. 2016A030313856, Shenzhen Sci-Tech Fund No. JCYJ20170307110329106, and Jiangsu Qinglan Project (2017).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, X., Li, Y., Yang, A. et al. Bayesian semiparametric quantile regression modeling for estimating earthquake fatality risk. Empir Econ 58, 2085–2103 (2020). https://doi.org/10.1007/s00181-018-1615-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00181-018-1615-4

Keywords

JEL Classification

Search

Navigation