---
title: "Introduction to fitur"
author: "Thomas Roh"
date: "February 13, 2017"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to fitur}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, fig.height = 5, fig.width = 7)
library(fitur)
```

## Basic Function

fitur is a package to provide wrapper functions for fitting univariate distributions. The main function is `fit_univariate` where you can supply numeric data to the function along with the desired attributes of the distribution you want to fit. It returns a list object with the density, distribution, quantile, and random deviates functions based on the calculated parameters from the given numeric vector. The 
parameter estimation is done with MLE.

## Discrete Distributions

```{r discrete}
set.seed(42)
x <- rpois(1000, 3)
fitted <- fit_univariate(x, 'pois', type = 'discrete')
# density function
plot(fitted$dpois(x=0:10),
     xlab = 'x',
     ylab = 'dpois')
# distribution function
plot(fitted$ppois(seq(0, 10, 1)),
     xlab= 'x',
     ylab = 'ppois')
# quantile function
plot(fitted$qpois,
     xlab= 'x',
     ylab = 'qpois')
# sample from theoretical distribution
summary(fitted$rpois(100))
# estimated parameters from MLE
fitted$parameters
```

## Continuous Distributions

```{r continuous}
set.seed(24)
x <- rweibull(1000, shape = .5, scale = 2)
fitted <- fit_univariate(x, 'weibull')
# density function
plot(fitted$dweibull,
     xlab = 'x',
     ylab = 'dweibull')
# distribution function
plot(fitted$pweibull,
     xlab = 'x',
     ylab = 'pweibull')
# quantile function
plot(fitted$qweibull,
     xlab = 'x',
     ylab = 'qweibull')
# sample from theoretical distribution
summary(fitted$rweibull(100))
# estimated parameters from MLE
fitted$parameters
```

## Empirical Distributions

The package also allows users to specify empirical distributions. For discrete distributions, the function will not truncate any integer values  with the given
input. For continuous distributions, the function will create bins using the Freedman-Diaconis rule.

### Discrete

```{r empiricalDiscrete}
set.seed(562)
x <- rpois(100, 5)
empDis <- fit_empirical(x)
# probability density function
plot(empDis$dempDis(0:10),
    xlab = 'x',
    ylab = 'dempDis')
# cumulative distribution function
plot(x = 0:10,
    y = empDis$pempDis(0:10),
    #type = 'l',
    xlab = 'x',
    ylab = 'pempDis')
# quantile function
plot(x = seq(.1, 1, .1),
    y = empDis$qempDis(seq(.1, 1, .1)),
    type = 'p',
    xlab = 'x',
    ylab = 'qempDis')
# random sample from fitted distribution
summary(empDis$r(100))
empDis$parameters
```

### Continuous

```{r empiricalContinous}
set.seed(562)
x <- rexp(100, 1/5)
empCont <- fit_empirical(x)
# probability density function
plot(x = 0:10,
     y = empCont$dempCont(0:10),
     xlab = 'x',
     ylab = 'dempCont')
# cumulative distribution function
plot(x = 0:10,
     y = empCont$pempCont(0:10),
     #type = 'l',
     xlab = 'x',
     ylab = 'pempCont')
# quantile function
plot(x = seq(.1, 1, by = .1),
     y = empCont$qempCont(seq(.1, 1, by = .1)),
     type = 'p',
     xlab = 'x',
     ylab = 'qempCont')
# random sample from fitted distribution
summary(empCont$r(100))
empCont$parameters
```