m8 {StMoMo}

Create an M8 type extension of the Cairns-Blake-Dowd mortality model

Description

Utility function to initialise a StMoMo object representing the M8 extension of the Cairns-Blake-Dowd mortality model introduced in Cairns et al (2009).

Usage

m8(link = c("logit", "log"), xc)

Arguments

link

defines the link function and random component associated with the mortality model. "log" would assume that deaths follow a Poisson distribution and use a log link while "logit" would assume that deaths follow a Binomial distribution and a logit link. Note that the default is the logit link.

xc

constant defining the cohort age-modulating parameter.

Details

The created model is either a logit-Binomial or a log-Poisson version of the M8 model which has predictor structure

\eta_{xt} = \kappa_t^{(1)} + (x-\bar{x})\kappa_t^{(2)} + (x_c-x)\gamma_{t-x}

where \bar{x} is the average age in the data and x_c is a predefined constant. Identifiability of the model is accomplished by applying parameters constraint

\sum_c\gamma_c = 0.

Value

An object of class "StMoMo".

References

Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1-35.

See Also

StMoMo, central2initial, cbd, m6, m7

Examples

M8 <- m8(xc = 89)
wxt <- genWeightMat(55:89,  EWMaleData$years, clip = 3)
M8fit <- fit(M8, data = central2initial(EWMaleData), ages.fit = 55:89)
plot(M8fit, parametricbx = FALSE)