---
title: "Fitting Models fitdistrplus"
author: "Prof. Eric A. Suess"
format: 
  html:
    self-contained: true
---

## Fitting Models

Random sample from the normal distribution, estimate the parameters

simulated sample

```{r}
mu <- 43; sigma <- 5.97   # parameters
n <- 300

x <- rnorm(n, mu, sigma)

hist(x, probability = TRUE)
```

Estimate the parameters using MLE

```{r}
library(fitdistrplus)

plotdist(x, histo = TRUE, demp = TRUE)

fit.norm <- fitdist(x, "norm", method = "mle")
summary(fit.norm)

fit.gam <- fitdist(x, "gamma", method = "mle")
summary(fit.gam)
```

Plot the fitted model on the histogram

```{r}
denscomp(list(fit.norm, fit.gam), legendtext = c("Normal", "Gamma"))
```

```{r}
cdfcomp(list(fit.norm, fit.gam), legendtext = c("Normal", "Gamma"))
qqcomp(list(fit.norm, fit.gam), legendtext = c("Normal", "Gamma"))
```


Random sample from the exponential distribution, estimate the parameters

simulated sample

```{r}
lambda <- 11.34   # parameter
n <- 30

x <- rexp(n, rate = lambda)

hist(x, probability = TRUE)
```



Estimate the parameters using MLE

```{r}
plotdist(x, histo = TRUE, demp = TRUE)

fit.exp <- fitdist(x, "exp", method = "mle")
summary(fit.exp)

fit.gam <- fitdist(x, "gamma", method = "mle")
summary(fit.gam)
```

Plot the fitted model on the histogram

```{r}
denscomp(list(fit.exp, fit.gam), legendtext = c("Exponential", "Gamma"))
```

```{r}
cdfcomp(list(fit.exp, fit.gam), legendtext = c("Exponential", "Gamma"))
qqcomp(list(fit.exp, fit.gam), legendtext = c("Exponential", "Gamma"))
```