---
title: "Introduction to demofit"
output: 
  rmarkdown::html_vignette: 
    fig_width: 8 
    fig_height: 5
vignette: >
  %\VignetteIndexEntry{Introduction to demofit}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, message=FALSE}
library(demofit)
```

## Overview

The demofit package provides a unified framework for mortality modelling.

## Example: Mortality curve fitting - MC()

```{r}
x <- 60:89
set.seed(123); m <- 0.0000082*exp(0.10771*c(60:89)+rnorm(30,0,0.1))
fit <- MC(x=x,m=m,curve="gompertz")
plot(fit)
```

## Example: Mortality model fitting and forecasting - FCS()

```{r}
x <- 60:89
a <- c(-4.8499,-4.7676,-4.6719,-4.5722,-4.4847,-4.3841,-4.2813,-4.1863,-4.0861,-3.9962,
-3.8885,-3.7896,-3.6853,-3.5737,-3.4728,-3.3718,-3.2586,-3.1474,-3.0371,-2.9206,
-2.7998,-2.6845,-2.5653,-2.4581,-2.3367,-2.2159,-2.1017,-1.9941,-1.8821, -1.7697)
b <- c(0.0283,0.0321,0.0335,0.0336,0.0341,0.0358,0.0368,0.0403,0.0392,0.0395,
0.0396,0.0399,0.0397,0.0386,0.039,0.0375,0.0367,0.0368,0.035,0.0354,
0.0336,0.0323,0.0313,0.0295,0.0282,0.0265,0.024,0.0226,0.0219,0.0183)
k <- c(12.11,10.69,11.18,9.64,9.35,8.21,6.89,5.74,4.56,3.6,
3.27,2.04,1.11,-0.44,-1.05,-1.03,-1.84,-2.9,-4.03,-4.12,
-5.18,-5.64,-6,-6.51,-6.91,-6.9,-8.32,-8.53,-9.69,-9.31)
set.seed(123)
M <- exp(outer(k,b)+matrix(a,nrow=30,ncol=30,byrow=TRUE)+rnorm(900,0,0.035))
fit <- FCS(x=x,M=M,model="LC",curve="makeham",h=30,jumpoff=2)
plot(fit)
```

## Example: Two-population mortality model fitting and forecasting - CFMS()

```{r}
x <- 60:89
a1 <- c(-5.18,-5.12,-4.98,-4.92,-4.82,-4.73,-4.66,-4.53,-4.45,-4.35,
-4.26,-4.17,-4.05,-3.95,-3.84,-3.73,-3.65,-3.52,-3.40,-3.29,
-3.14,-3.02,-2.88,-2.76,-2.64,-2.49,-2.37,-2.25,-2.12,-2.00)
a2 <- c(-4.78,-4.68,-4.57,-4.49,-4.39,-4.29,-4.19,-4.10,-4.00,-3.89,
-3.80,-3.69,-3.60,-3.49,-3.39,-3.29,-3.17,-3.07,-2.96,-2.85,
-2.71,-2.62,-2.49,-2.37,-2.26,-2.14,-2.04,-1.91,-1.82,-1.72)
B <- c(0.0381,0.0340,0.0420,0.0389,0.0423,0.0414,0.0406,0.0393,0.0415,0.0400,
0.0411,0.0362,0.0387,0.0381,0.0384,0.0385,0.0356,0.0314,0.0317,0.0337,
0.0316,0.0298,0.0284,0.0270,0.0248,0.0262,0.0205,0.0215,0.0142,0.0145)
K <- c(9.66,9.89,10.66,9.83,9.52,7.39,7.64,6.36,2.32,4.18,
2.91,-0.61,0.28,-0.38,-1.79,-3.34,-1.74,-3.50,-4.28,-4.77,
-4.98,-7.13,-5.09,-6.41,-5.56,-5.65,-6.12,-5.64,-7.35,-6.28)
b1 <- c(0.0012,-0.0033,0.0523,0.0161,0.0529,0.0220,0.0312,0.0437,0.0709,0.0444,
0.0398,0.0361,0.0403,0.0396,0.0506,0.0315,0.0428,0.0261,0.0384,0.0388,
0.0300,0.0269,0.0275,0.0256,0.0239,0.0421,0.0314,0.0284,0.0174,0.0314)
k1 <- c(-1.24,-1.38,-3.48,-2.51,-1.32,-1.90,-3.42,-0.94,0.24,-0.48,
-0.26,2.70,1.39,-0.46,1.74,2.53,0.90,1.43,0.76,2.48,
0.74,2.32,0.42,1.69,-0.64,1.30,0.19,-0.69,-1.11,-1.01)
b2 <- c(-0.0014,0.0272,0.0083,0.0273,0.0209,0.0253,0.0144,0.0333,0.0460,0.0439,
0.0439,0.0674,0.0331,0.0443,0.0312,0.0240,0.0570,0.0312,0.0403,0.0376,
0.0500,0.0289,0.0466,0.0418,0.0349,0.0149,0.0366,0.0178,0.0361,0.0372)
k2 <- c(2.35,0.62,-0.38,0.12,0.00,0.80,-1.39,0.38,2.47,0.40,
0.76,3.06,1.42,-0.73,0.79,1.94,0.12,0.60,-0.43,0.29,
0.17,0.98,-1.01,-0.13,-2.46,-1.24,-1.65,-2.48,-2.32,-3.06)
set.seed(123)
M1 <- exp(outer(k1,b1)+outer(K,B)+matrix(a1,nrow=30,ncol=30,byrow=TRUE)+rnorm(900,0,0.07))
M2 <- exp(outer(k2,b2)+outer(K,B)+matrix(a2,nrow=30,ncol=30,byrow=TRUE)+rnorm(900,0,0.07))
fit <- CFMS(x=x,M1=M1,M2=M2,curve="makeham",h=30,jumpoff=2)
plot(fit)
```

## Example: Mortality ensemble interval forecasting - ENI()

```{r}
x <- 60:69
a <- c(-4.8499,-4.7676,-4.6719,-4.5722,-4.4847,-4.3841,-4.2813,-4.1863,-4.0861,-3.9962)
b <- c(0.0801,0.0909,0.0948,0.0951,0.0965,0.1014,0.1042,0.1141,0.1110,0.1118)
k <- c(12.11,10.69,11.18,9.64,9.35,8.21,6.89,5.74,4.56,3.60,
3.27,2.04,1.11,-0.44,-1.05,-1.03,-1.84,-2.90,-4.03,-4.12,
-5.18,-5.64,-6.00,-6.51,-6.91,-6.90,-8.32,-8.53,-9.69,-9.31)
set.seed(123)
M <- exp(outer(k,b)+matrix(a,nrow=30,ncol=10,byrow=TRUE)+rnorm(300,0,0.035))
fit1 <- LCS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit2 <- RHS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit3 <- APCS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit4 <- CBDS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
fit <- ENI(fit1,fit2,fit3,fit4)
plot(fit)
```
