---
title: "A Case Study Using the Beta-Danish Distribution"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{A Case Study Using the Beta-Danish Distribution}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = '#>')
```

# Introduction

This vignette demonstrates a typical survival analysis workflow using the BetaDanish package.

```{r}
library(BetaDanish)
library(survival)
data('remission', package = 'BetaDanish')
head(remission)
```

# Fitting the Beta-Danish model

```{r}
fit <- fit_betadanish(Surv(time, status) ~ 1, data = remission, n_starts = 1)
summary(fit)
```

# Three-parameter submodel

```{r}
fit_sub <- fit_betadanish(Surv(time, status) ~ 1, data = remission, submodel = TRUE, n_starts = 1)
compare_models(fit, fit_sub)
```

# Diagnostic plots

```{r, fig.width = 7, fig.height = 5}
plot(fit, type = 'survival')
plot(fit, type = 'hazard')
```

# Interpretation

The fitted model can be used to estimate survival probabilities, hazard behavior, and overall model fit. Users should compare the Beta-Danish model with alternative lifetime distributions and inspect diagnostic plots before drawing final conclusions.