Abstract
We develop a new R package that computes the probability density function, the hazard rate function, the integrated hazard rate function, and the quantile function for forty four survival models commonly used in actuarial science. A real data application of the package is illustrated. It is hoped that this package could be useful for actuarial scientists.
Similar content being viewed by others
References
Bain LJ (1974) Analysis for the linear failure-rate life-testing distribution. Technometrics 16:551–559
Beard RE (1959) Note on some mathematical mortality models. In: Wolstenholme GEW, O’Connor M (eds) The lifespan of animals. Little Brown, Boston, pp 302–311
Bebbington M, Goddard M, Lai CD, Zitikis R (2009) Identifying health inequalities between Maori and non-Maori using mortality tables. Kotuitui N Z J Soc Sci 4:103–114
Bebbington M, Lai CD, Zitikis R (2007) A flexible Weibull extension. Reliab Eng Syst Saf 92:719–726
Beirlant J, Goegebeur Y, Verlaak R, Vynckier P (1998) Burr regression and portfolio segmentation. Insur Math Econ 23:231–250
Borovkov KA, Dickson DCM (2008) On the ruin time distribution for a Sparre Andersen process with exponential claim sizes. Insur Math Econ 42:1104–1108
Cerezo EC, Bielsa MMC, Ramon MC (2011) Actuarial theory of the losses measurement by exposure to credit risk: an application to the Colombian market. Academia-Revista Latinoamericana de Administracion 47:112–125
Chen N, Zhao LQ, Luo CD (2009) A truncated distribution commonly-used in non-life insurance. In: Zhu K, Zhang H (eds) Recent advance in statistics application and related areas, pp 230–234
Chen Z (2000) A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Stat Prob Lett 49:155–161
Choquet R, Viallefont A, Rouan L, Gaanoun K, Gaillard JM (2011) A semi-Markov model to assess reliably survival patterns from birth to death in free-ranging populations. Methods Ecol Evol 2:383–389
Choudhury A (2005) A simple derivation of moments of the exponentiated Weibull distribution. Metrika 62:17–22
de Moivre A (1738) The doctrine of chances. ISBN 0821821032
Fiocco M, Putter H, van Houwelingen JC (2005) Reduced rank proportional hazards model for competing risks. Biostatistics 6:465–478
Gauss CF (1809) Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm (in Latin)
Gompertz B (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans R Soc Lond 115:513–583
Gumbel EJ (1954) Statistical theory of extreme values and some practical applications. Applied Mathematics Series, vol 33, US Department of Commerce, National Bureau of Standards
Gupta RD, Kundu D (1999) Generalized exponential distributions. Aust N Z J Stat 41:173–188
Gupta RD, Kundu D (2001) Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biometric J 43:117–130
Haberman S, Renshaw A (2011) A comparative study of parametric mortality projection models. Insur Math Econ 48:35–55
Hawkes K, Smith KR, Blevins JK (2012) Human actuarial aging increases faster when background death rates are lower: a consequence of differential heterogeneity? Evolution 66:103–114
Hernandez-Bastida A, Fernandez-Sanchez MP, Gomez-Deniz E (2011) Collective risk model: Poisson-Lindley and exponential distributions for Bayes premium and operational risk. J Stat Comput Simul 81:759–778
Hjorth U (1980) Reliability distribution with increasing, decreasing, constant and bathtub-shaped failure rates. Technometrics 17:99–107
Hocht S, Zagst R (2010) Pricing distressed CDOs with stochastic recovery. Rev Deriv Res 13:219–244
Jang J, Fu GY (2008) Transform approach for operational risk modeling: value-at-risk and tail conditional expectation. J Oper Risk 3:45–61
Jones BL, Mereu JA (2002) A critique of fractional age assumptions. Insur Math Econ 30:363–370
Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481
Kleiber C, Kotz S (2003) Statistical size distributions in economics and actuarial sciences. Wiley, Hoboken
Klutke GA, Kiessler PC, Wortman MA (2003) A critical look at the bathtub curve. IEEE Trans Reliab 52:125–129
Kumaraswamy P (1980) Generalized probability density function for double-bounded random processes. J Hydrol 46:79–88
Kundu D, Raqab M (2005) Generalized Rayleigh distribution: different methods of estimations. Comput Stat Data Anal 49:187–200
Lai CD, Xie M, Murthy DNP (2003) Modified Weibull distribution. IEEE Trans Reliab 52:33–37
Lan Y, Leemis LM (2008) The logistic-exponential survival distribution. Nav Res Logist 55:252–264
Landers TL, Martin K, English JR (1994) Decision modeling for thermal stress screening of commercial electronics. Microelectron Reliab 34:1643–1656
Lenart A (2012) The moments of the Gompertz distribution and maximum likelihood estimation of its parameters. Scand Actuar J. doi:10.1080/03461238.2012.687697
Makeham WM (1859) On the law of mortality and the construction of annuity tables. J Inst Actuar 8:301–310
Marshall AW, Olkin I (1997) A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84:641–652
Matis TI, Jayaraman R, Rangan A (2008) Optimal price and pro rata decisions for combined warranty policies with different repair options. IIE Trans 40:984–991
Mierzejewski F (2011) A model of equilibrium in markets of cash balances. IMA J Manag Math 22: 253–270
Mudholkar GS, Srivastava DK (1993) Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab 42:299–302
Mudholkar GS, Srivastava DK, Freimer M (1995) The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 37:436–445
Nadarajah S (2009) Bathtub-shaped failure rate functions. Qual Quant 43:855–863
Nadarajah S, Gupta AK (2005) On the moments of the exponentiated Weibull distribution. Commun Stat Theory Methods 34:253–256
Nadarajah S, Haghighi F (2011) An extension of the exponential distribution. Statistics 45:543–558
Nikulin M, Haghighi F (2006) A chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data. J Math Sci 133:1333–1341
Pareto V (1964) Cours d’économie politique. Nouvelle édition par G-H Bousquet et G Busino. Librairie Droz, Geneva, pp 299–345
Perks W (1932) On some experiments in the graduation of mortality statistics. J Inst Actuar 63:12–40
Pham H (2002) A Vtub-shaped hazard rate function with applications to system safety. Int J Reliab Appl 3:1–16
Pham H (2011) Modeling US mortality and risk-cost optimization on life expectancy. IEEE Trans Reliab 60:125–133
Ping H, Xiang W (2009) Discrete life insurance actuarial models with variable interest rate based on de Moivre’s and Makeham’s law of mortality. In: Luo Q, Wang B (eds) Proceedings of the 2009 international Asia symposium on intelligent interaction and affective computing, pp 160–163
Prentice RL (1975) Discrimination among some parametric models. Biometrika 62:607–614
R Development Core Team (2011) A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria
Raqab MZ, Kundu D (2006) Burr type X distribution: revisited. J Probab Stat Sci 4:179–193
Richards SJ (2008) Applying survival models to pensioner mortality data. Br Actuar J 14:257–303
Richards SJ (2012) A handbook of parametric survival models for actuarial use. Scand Actuar J. doi:10.1080/03461238.2010.506688
Sarabia JM, Castillo E (2005) About a class of max-stable families with applications to income distributions. Metron LXIII:505–527
Sarhan AM, Kundu D (2009) Generalized linear failure rate distribution. Commun Stat Theory Methods 38:642–660
Schabe H (1994) Constructing lifetime distributions with bathtub shaped failure rate from DFR distributions. Microelectron Reliab 34:1501–1508
Schulzer M, Mak E, Calne DB (1992) The antiparkinson efficacy of deprenyl derives from transient improvement that is likely to be symptomatic. Ann Neurol 32:795–798
Shirke DT, Kumbhar RR, Kundu D (2005) Tolerance intervals for exponentiated scale family of distributions. J Appl Stat 32:1067–1074
Stacy EW (1962) A generalization of the gamma distribution. Ann Math Stat 33:1187–1192
Thampi KK, Jacob MJ (2008) Moments of the time of ruin in a renewal risk model with discounted penalty. J Risk Financ 9:173–187
Topp CW, Leone FC (1955) A family of \(J\)-shaped frequency functions. J Am Stat Assoc 50:209–219
van Dorp JR, Kotz S (2006) Modeling income distributions using elevated distributions on a bounded domain. In: Pleguezeoulo RH, Cespedes JC, Velasco JMH (eds) Distribution models theory, pp 1–25
Verhoef C (2002) Quantitative IT portfolio management. Sci Comput Program 45:1–96
Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297
Xie M, Lai CD (1995) Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliab Eng Syst Saf 52:87–93
Xie M, Tang Y, Goh TN (2002) A modified Weibull extension with bathtub-shaped failure rate function. Reliab Eng Syst Saf 76:279–285
Acknowledgments
The authors would like to thank the Editor-in-Chief, the Associate Editor and the two referees for careful reading and for comments which greatly improved the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nadarajah, S., Bakar, S.A.A. A new R package for actuarial survival models. Comput Stat 28, 2139–2160 (2013). https://doi.org/10.1007/s00180-013-0400-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00180-013-0400-2