---
title: "Problem 46: Bowhead whale."
author: "Prof. Eric A. Suess"
format:
  html:
    self-contained: true
---

## Problem 46: Bowhead whale.



```{r}
library(readr)

whale <- read_csv("~/classes/2023-2024/Fall 2023/Stat640/website/_homework/mle/whale/whale.csv")
head(whale)
```

convert the data_frame to a vector

The fitdistrplus package expects a vector as input.

```{r}
whale <- whale$times
whale
```

```{r}
library(fitdistrplus)
```


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

fit gamma using MME and MLE

```{r}
fit.gamma.mme <- fitdist(whale, "gamma", method = "mme")
summary(fit.gamma.mme)

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

plot the log-likelihood

```{r}
llplot(fit.gamma.mle)
llplot(fit.gamma.mle, expansion = 2)
```

compare

```{r}
denscomp(list(fit.gamma.mme, fit.gamma.mle), legendtext = c("MME", "MLE"))
```

```{r}
cdfcomp(list(fit.gamma.mme, fit.gamma.mle), legendtext = c("MME", "MLE"))
qqcomp(list(fit.gamma.mme, fit.gamma.mle), legendtext = c("MME", "MLE"))
```

bootstrap the MME

```{r}
b1 <- bootdist(fit.gamma.mme, niter=101)
print(b1)
```

```{r}
plot(b1)
```

```{r}
hist(b1$estim$shape)
hist(b1$estim$rate)
```

```{r}
summary(b1)
```

bootstrap the MLE

```{r}
b2 <- bootdist(fit.gamma.mle, niter=101)
print(b2)
```

```{r}
hist(b2$estim$shape)
hist(b2$estim$rate)
```

```{r})
plot(b2)
```

```{r}
summary(b2)
```