PCBDS: Poisson CBD model
In demofit: Parametric Mortality Curve Fitting and Mortality Forecasting Tools

PCBDS

R Documentation

Poisson CBD model

Description

Fits and forecasts mortality rates using CBD model with Poisson assumption.

Usage

PCBDS(
  x,
  D,
  E,
  curve = c("gompertz", "makeham", "perks", "weibull", "beard", "martinelle", "thatcher",
    "gompertz2", "makeham2", "perks2", "weibull2", "beard2", "martinelle2", "thatcher2"),
  h = 10,
  jumpoff = 1
)

Arguments

`x`	vector of ages.
`D`	matrix of death counts (rows as years and columns as ages).
`E`	matrix of mid-year exposures (rows as years and columns as ages).
`curve`	name of mortality curve for smoothing forecasted mortality rates (including gompertz, makeham, perks, weibull, beard, martinelle, thatcher, gompertz2, makeham2, perks2, weibull2, beard2, martinelle2, thatcher2, where first 7 curves' parameters are unconstrained and last 7 curves' parameters are generally restricted to be positive).
`h`	forecast horizon (default = 10).
`jumpoff`	if 1, forecasts are based on estimated parameters only; if 2, forecasts are anchored to observed mortality rates in final year (default = 1).

Details

The CBD (M5) model with Poisson assumption is specified as

ln(m_{x,t}) = \kappa_{1,t} + \kappa_{2,t} (x-\bar{x}) and D_{x,t} ~ Poisson(E_{x,t} m_{x,t}).

The model is estimated by Newton updating scheme and is forecasted by ARIMA applied to \kappa_{1,t} and \kappa_{2,t}. It is designed for ages 50-90.

Value

An object of class PCBDS with associated S3 methods coef, forecast (which = 1 for smoothed (default); which = 2 for raw), plot, and residuals.

References

Cairns, A.J.G., Blake, D., and Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73(4), 687-718.

Examples

x <- 60:89
k1 <- -2.97-0.0245*(0:29)
k2 <- 0.101+0.000345*(0:29)
set.seed(123)
M <- exp(matrix(k1,nrow=30,ncol=30,byrow=FALSE)+outer(k2,(x-mean(x)))+rnorm(900,0,0.035))
E <- matrix(c(107788,108036,107481,106552,104608,100104,95803,91345,84980,79557,
75146,70559,65972,60898,55623,50522,47430,45895,41443,34774,
30531,27754,25105,22271,19437,16888,14458,12146,10038,7994),30,30,byrow=TRUE)
D <- round(E*M)
fit <- PCBDS(x=x,D=D,E=E,curve="makeham",h=30,jumpoff=2)
coef(fit)
forecast::forecast(fit)
plot(fit)
residuals(fit)

demofit documentation built on June 12, 2026, 1:07 a.m.