---
title: "Introduction to smmR"
output: rmarkdown::html_vignette
description: >
  This will help you start with smmR. Some functions are exposed here,
  but do not hesitate to go further navigating the reference.
vignette: >
  %\VignetteIndexEntry{Introduction to smmR}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup, include=FALSE}
library(knitr)
knitr::opts_chunk$set(
    fig.align = "center",
    fig.height = 5.5,
    fig.width = 6,
    warning = FALSE,
    collapse = TRUE,
    dev.args = list(pointsize = 10),
    out.width = "65%"
)
```

Start by loading the needed libraries:
```r
library(smmR)
```

In our case, we will need a special distribution:
```r
library(DiscreteWeibull)
```

Then, let us create a **smmparametric** object to represent the semi-Markov chain associated to the system:
```r
# State space
states <- c("1", "2", "3")
# Initial distribution
alpha <- c(1, 0, 0)
# Transition matrix
p <- matrix(data = c(0, 1, 0, 
                     0.95, 0, 0.05, 
                     1, 0, 0), nrow = 3, byrow = TRUE)
# Distribution matrix
distr <- matrix(c(NA, "geom", NA, 
                  "dweibull", NA, "dweibull", 
                  "dweibull", NA, NA), 
                nrow = 3, ncol = 3, byrow = TRUE)
param1 <- matrix(c(NA, 0.8, NA, 
                   0.3, NA, 0.5,
                   0.6, NA, NA), 
                 nrow = 3, ncol = 3, byrow = TRUE)
param2 <- matrix(c(NA, NA, NA, 
                   0.5, NA, 0.7,
                   0.9, NA, NA), 
                 nrow = 3, ncol = 3, byrow = TRUE)
parameters <- array(c(param1, param2), c(3, 3, 2))
# Create smmparametric model
factory <- smmparametric(states = states, init = alpha, ptrans = p, 
                         type.sojourn = "fij", distr = distr, param = parameters)
```

After that, we are able to simulate a sequence of sample sizes $M = 10,000$:

```r
M <- 10000
seq <- simulate(object = factory, nsim = M)
```

Thanks to the `smmR` package, we can estimate any semi-Markov model
with one or several discrete sequences. In our case, we are going to
introduce a **non-parametric estimation**:

```r
estimate <- fitsmm(sequences = seq, states = states, type.sojourn = "fij")
```

The estimate $\hat{p}$ of the transition matrix $p$ is:

```r
print(x = estimate$ptrans, digits = 2)
```

See the vignette `textile-factory` for more details.