model_distributions.Rmd

---
title: "Manipulation des distributions"
author: "State of the R"
date: "24-28/08/2020"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r}
library(distributional)
library(ggplot2)
theme_set(theme_minimal())
```

# Utilisation basique

Création d'une loi normale

```{r}
dn <- dist_normal(mu = 5, sigma = 2)
dn
class(dn)
```

Quelques quantités d'intérêt

```{r}
list(mean = mean(dn), median = median(dn), variance = variance(dn), 
     skewness = skewness(dn), kurtosis = kurtosis(dn))
```

Courbes

```{r, warning=FALSE}
autoplot(dn) 
```

Intervalles

```{r}
hilo(dn) # intervalle de confiance
hdr(dn) # intervalle du ou des modes
```

Échantillonage

```{r}
sample <- generate(dn, times = 10)
sample
likelihood(dn, sample)
```

```{r}
cdf(dn, 5)
quantile(dn, 0.5)
```


Calculs

```{r}
2 * dn - 5 
dn ^ 2 # ne connait pas
```

# Vecteur de distribution

```{r}
dchi <- dist_chisq(df = 5)
dt <- dist_student_t(df = 10)
dm <- dist_mixture(dt, dn, weights = c(0.6, 0.4))
dvec <- c(dn, dchi, dt, dm)
dvec
autoplot(dvec)
mean(dvec)
variance(dvec)
hilo(dvec, size = 66)
cdf(dvec, 5)
```

# Graphiques

```{r}
library(ggdist)
df <- data.frame(name = factor(c("N(5,4)", "\u1d6a²(5)", "t(10, 0, 1)", "Mixture"), 
                               levels = c("N(5,4)", "\u1d6a²(5)", "t(10, 0, 1)", "Mixture")),
                 dist = dvec)
df
ggplot(df) +
  aes(y = name, dist = dist, fill = name) +
  stat_dist_halfeye(show.legend = FALSE, .width = c(0.66, 0.95)) +
  labs(x = NULL, y = NULL)
ggplot(df) +
  aes(y = name, dist = dist, fill = name) +
  stat_dist_gradientinterval(show.legend = FALSE) +
  labs(x = NULL, y = NULL)
ggplot(df) +
  aes(y = name, dist = dist, fill = name) +
  stat_dist_dots(quantiles = 150, show.legend = FALSE) +
  labs(x = NULL, y = NULL)
```

# Lois discretes

```{r}
dp <- dist_poisson(4)
dp
mean(dp)
generate(dp, 10)
```

Loi inflatée

```{r}
dpi <- dist_inflated(dp, 0.5, x = 0)
dpi
mean(dpi)
generate(dpi, 10)
```


# Distribution disponibles

```{r}
ls("package:distributional", pattern = "^dist_")
```