availableLaws: Check Available Mortality Laws

Description Usage Arguments Value Author(s) References See Also Examples

View source: R/availableLaws.R

Description

The function returns information about the parametric models that can be called and fitted in the MortalityLaw function. For a comprehensive review of the most important mortality laws, Tabeau (2001) is a good starting point.

Usage

1

Arguments

law

Optional. Default: NULL. One can extract details about a certain model by specifying its codename.

Value

The output is of the "availableLaws" class with the components:

table

Table with mortality models and codes to be used in MortalityLaw

legend

Table with details about the section of the mortality curve

Author(s)

Marius D. Pascariu

References

  1. 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. Philosophical Transactions of the Royal Society of London, 115, 513-583.

  2. Makeham, W. (1860). On the Law of Mortality and Construction of Annuity Tables. The Assurance Magazine and Journal of the Institute of Actuaries, 8(6), 301-310.

  3. Thiele, T. (1871). On a Mathematical Formula to express the Rate of Mortality throughout the whole of Life, tested by a Series of Observations made use of by the Danish Life Insurance Company of 1871. Journal of the Institute of Actuaries and Assurance Magazine, 16(5), 313-329.

  4. Oppermann, L. H. F. (1870). On the graduation of life tables, with special application to the rate of mortality in infancy and childhood. The Insurance Record Minutes from a meeting in the Institute of Actuaries., 42.

  5. Wittstein, T. and D. Bumsted. (1883). The Mathematical Law of Mortality. Journal of the Institute of Actuaries and Assurance Magazine, 24(3), 153-173.

  6. Steffensen, J. (1930). Infantile mortality from an actuarial point of view. Skandinavisk Aktuarietidskrift 13, 272-286.

  7. Perks, W. (1932). On Some Experiments in the Graduation of Mortality Statistics. Journal of the Institute of Actuaries, 63(1), 12-57.

  8. Harper, F. S. (1936). An actuarial study of infant mortality. Scandinavian Actuarial Journal 1936 (3-4), 234-270.

  9. Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of applied mechanics 103, 293-297.

  10. Beard, R. E. (1971). Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes. Biological aspects of demography 999, 57-68.

  11. Vaupel, J., Manton, K.G., and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3): 439-454.

  12. Siler, W. (1979), A Competing-Risk Model for Animal Mortality. Ecology, 60: 750-757.

  13. Heligman, L., & Pollard, J. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107(1), 49-80.

  14. Rogers A and Planck F (1983). MODEL: A General Program for Estimating Parametrized Model Schedules of Fertility, Mortality, Migration, and Marital and Labor Force Status Transitions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-83-102

  15. Martinelle S. (1987). A generalized Perks formula for old-age mortality. Stockholm, Sweden, Statistiska Centralbyran, 1987. 55 p. (R&D Report, Research-Methods-Development, U/STM No. 38)

  16. Carriere J.F. (1992). Parametric models for life tables. Transactions of the Society of Actuaries. Vol.44

  17. Kostaki A. (1992). A nine-parameter version of the Heligman-Pollard formula. Mathematical Population Studies. Vol. 3 277-288

  18. Thatcher AR, Kannisto V and Vaupel JW (1998). The force of mortality at ages 80 to 120. Odense Monographs on Population Aging Vol. 5 Odense University Press, 1998. 104, 20 p. Odense, Denmark

  19. Tabeau E. (2001) A Review of Demographic Forecasting Models for Mortality. In: Tabeau E., van den Berg Jeths A., Heathcote C. (eds) Forecasting Mortality in Developed Countries. European Studies of Population, vol 9. Springer, Dordrecht

  20. Finkelstein M. (2012) Discussing the Strehler-Mildvan model of mortality Demographic Research, Vol. 26(9), 191-206.

See Also

MortalityLaw

Examples

1

Example output

Mortality laws available in the package:

 YEAR NAME            
 1825 Gompertz        
 <NA> Gompertz        
 <NA> Inverse-Gompertz
 1860 Makeham         
 <NA> Makeham         
 1870 Opperman        
 1871 Thiele          
 1883 Wittstein       
 1932 Perks           
 1939 Weibull         
 <NA> Inverse-Weibull 
 1943 Van der Maen    
 1943 Van der Maen    
 1960 Strehler-Mildvan
 <NA> Quadratic       
 1971 Beard           
 1971 Beard-Makeham   
 1979 Gamma-Gompertz  
 1979 Siler           
 1980 Heligman-Pollard
 1980 Heligman-Pollard
 1980 Heligman-Pollard
 1980 Heligman-Pollard
 1983 Rogers-Planck   
 1987 Martinelle      
 1992 Carriere        
 1992 Carriere        
 1992 Kostaki         
 1998 Kannisto        
 1998 Kannisto-Makeham
 MODEL                                                                    TYPE
 mu[x] = A exp[Bx]                                                        3   
 mu[x] = 1/sigma * exp[(x-M)/sigma)]                                      3   
 mu[x] = [1- exp(-(x-M)/sigma)] / [exp(-(x-M)/sigma) - 1]                 2   
 mu[x] = A exp[Bx] + C                                                    3   
 mu[x] = 1/sigma * exp[(x-M)/sigma)] + C                                  3   
 mu[x] = A/sqrt(x) - B + C*sqrt(x)                                        1   
 mu[x] = A exp(-Bx) + C exp[-.5D (x-E)^2] + F exp(Gx)                     6   
 q[x] = (1/B) A^-[(Bx)^N] + A^-[(M-x)^N]                                  6   
 mu[x] = [A + BC^x] / [BC^-x + 1 + DC^x]                                  3   
 mu[x] = 1/sigma * (x/M)^(M/sigma - 1)                                    1   
 mu[x] = 1/sigma * (x/M)^[-M/sigma - 1] / [exp((x/M)^(-M/sigma)) - 1]     2   
 mu[x] = A + Bx + Cx^2 + I/[N - x]                                        4   
 mu[x] = A + Bx + I/[N - x]                                               5   
 mu[x] = K * exp[-V0 * (1 - Bx)/D]                                        3   
 mu[x] = A + Bx + Cx^2                                                    5   
 mu[x] = A exp(Bx) / [1 + KA exp(Bx)]                                     4   
 mu[x] = A exp(Bx) / [1 + KA exp(Bx)] + C                                 4   
 mu[x] = A exp(Bx) / (1 + AG/B * [exp(Bx) - 1])                           4   
 mu[x] = A exp(-Bx) + C + D exp(Ex)                                       6   
 q[x]/p[x] = A^[(x + B)^C] + D exp[-E log(x/F)^2] + G H^x                 6   
 q[x] = A^[(x + B)^C] + D exp[-E log(x/F)^2] + GH^x / [1 + GH^x]          6   
 q[x] = A^[(x + B)^C] + D exp[-E log(x/F)^2] + GH^x / [1 + KGH^x]         6   
 q[x] = A^[(x + B)^C] + D exp[-E log(x/F)^2] + GH^(x^K) / [1 + GH^(x^K)]  6   
 q[x] = A0 + A1 exp[-Ax] + A2 exp[B(x - u) - exp(-C(x - u))] + A3 exp[Dx] 6   
 mu[x] = [A exp(Bx) + C] / [1 + D exp(Bx)] + K exp(Bx)                    6   
 l[x] = P1 l[x](weibull) + P2 l[x](invweibull) + P3 l[x](gompertz)        6   
 l[x] = P1 l[x](weibull) + P2 l[x](invgompertz) + P3 l[x](gompertz)       6   
 q[x]/p[x] = A^[(x+B)^C] + D exp[-(E_i log(x/F_))^2] + G H^x              6   
 mu[x] = A exp(Bx) / [1 + A exp(Bx)]                                      5   
 mu[x] = A exp(Bx) / [1 + A exp(Bx)] + C                                  5   
 CODE            
 gompertz        
 gompertz0       
 invgompertz     
 makeham         
 makeham0        
 opperman        
 thiele          
 wittstein       
 perks           
 weibull         
 invweibull      
 vandermaen      
 vandermaen2     
 strehler_mildvan
 quadratic       
 beard           
 beard_makeham   
 ggompertz       
 siler           
 HP              
 HP2             
 HP3             
 HP4             
 rogersplanck    
 martinelle      
 carriere1       
 carriere2       
 kostaki         
 kannisto        
 kannisto_makeham

LEGEND:
 TYPE Coverage                      
 1    Infant mortality              
 2    Accident hump                 
 3    Adult mortality               
 4    Adult and/or old-age mortality
 5    Old-age mortality             
 6    Full age range                

MortalityLaws documentation built on Sept. 16, 2020, 5:08 p.m.