plot.fitLCmulti {CvmortalityMult}

Function to plot the parameters of the multi-population mortality models

Description

R function to plot the parameters for the Additive (Debon et al., 2011) and Multiplicative (Russolillo et al., 2011) Multi-Population mortality model. It should be mentioned that in case that this function is developed for fitting several populations. However, in case you only consider one population, the function will fit the one-population Lee-Carter model (Lee and Carter, 1992).

Usage

## S3 method for class 'fitLCmulti'
plot(x, ...)

Arguments

x

x developed using function fitLCmulti() which are objects of the fitLCmulti class.

...

additional arguments to show in the plot appearance.

Value

plot the different parameters for the multi-population mortality models ax, bx, kt and Ii. This function is valid for both approaches Additive and Multiplicative multi-population mortality models.

References

Debon, A., Montes, F., & Martinez-Ruiz, F. (2011). Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions. European Actuarial Journal, 1, 291-308.

Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671.

Multi-population mortality model developed by: Russolillo, M., Giordano, G., & Haberman, S. (2011). Extending the Lee–Carter model: a three-way decomposition. Scandinavian Actuarial Journal, 2011(2), 96-117.

See Also

fitLCmulti, forecast.fitLCmulti, plot.forLCmulti, multipopulation_cv, multipopulation_loocv

Examples

#The example takes more than 5 seconds because it includes
#several fitting and forecasting process and hence all
#the process is included in donttest

#First, we present the data that we are going to use
SpainRegions
ages <- c(0, 1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90)

library(gnm)
library(forecast)
#ADDITIVE MULTI-POPULATION MORTALITY MODEL
#In the case, the user wants to fit the additive multi-population mortality model
additive_Spainmales <- fitLCmulti(model = "additive",
                              qxt = SpainRegions$qx_male,
                              periods = c(1991:2020),
                              ages = c(ages),
                              nPop = 18,
                              lxt = SpainRegions$lx_male)

additive_Spainmales

#If the user does not provide the model inside the function fitLCmult()
#the multi-population mortality model applied will be additive one.

#Once, we have fit the data, it is possible to see the ax, bx, kt, and Ii
#provided parameters for the fitting.
plot(additive_Spainmales)

#MULTIPLICATIVE MULTI-POPULATION MORTALITY MODEL
#In the case, the user wants to fit the multiplicative multi-population mortality model
multiplicative_Spainmales <- fitLCmulti(model = "multiplicative",
                              qxt = SpainRegions$qx_male,
                              periods = c(1991:2020),
                              ages = c(ages),
                              nPop = 18,
                              lxt = SpainRegions$lx_male)

multiplicative_Spainmales

#Once, we have fit the data, it is possible to see the ax, bx, kt, and It
#provided parameters for the fitting.
plot(multiplicative_Spainmales)

#LEE-CARTER FOR SINGLE-POPULATION
#As we mentioned in the details of the function, if we only provide the data
#from one-population the function fitLCmulti()
#will fit the Lee-Carter model for single populations.
LC_Spainmales <- fitLCmulti(qxt = SpainNat$qx_male,
                              periods = c(1991:2020),
                              ages = ages,
                              nPop = 1)

LC_Spainmales

#Once, we have fit the data, it is possible to see the ax, bx, and kt
#parameters provided for the single version of the LC.
plot(LC_Spainmales)