---
title: "Introduction to NPFD"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to NPFD}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  message = FALSE,
  warning = FALSE,
  fig.width = 7,
  fig.height = 5
)
```

```{r library setup}
library(NPFD)
library(siggenes)
library(KernSmooth)
library(splines)
library(stats)
library(graphics)
library(VGAM)
```


# Introduction

The NPFD package provides tools for performing deconvolution using the NPFD (N-Power Fourier Deconvolution) method described in a submitted paper by the author. This package is designed to make it easy to apply the NPFD method in R for various data sets.

NPFD is thoroughly documented in the paper, including detailed mathematical derivations, theoretical background, and several examples. We recommend referring to the paper for in-depth understanding and theoretical details.


# Overview of Functions

The main functions included in the NPFD package are:

- deconvolve(): This is the primary function of the package, which performs deconvolution on the provided data.
- densprf(): This function is used internally by deconvolve() for density estimation.
- createSample(): This function creates a sample from a centered distribution when a replicate of the mixed data is provided.

The and denspr() function is sourced from the 'siggenes' package, with densprf() being a tailored modification of the original denspr() function. Below, we provide a brief example of how to use the deconvolve() function.

```{r example setup}
set.seed(123)
x <- rnorm(1000)
y <- rgamma(1000, 10, 2)
z <- x + y

independent.x <- rnorm(100)

fy.NPFD <- deconvolve(independent.x, z, calc.error = T, plot = T)
fy <- denspr(y, addx = T)

fy.NPFD$N
fy.NPFD$error

plot(NULL, xlim = range(y), ylim = c(0, max(fy$y, fy.NPFD$y)), xlab = "x", ylab = "density")
lines(fy, col = "blue", lwd = 2)
lines(fy.NPFD, col = "orange", lwd = 2)
legend("topright", legend = c(expression(f[y]), expression(f[y]^{NPFD})), 
       col = c("blue", "orange"), lwd = c(2, 2))
```


# References

For more detailed information on the methods used in this package, please refer to the following publications:

Anarat A., Krutmann, J., and Schwender, H. (2024). A nonparametric statistical method for deconvolving densities in the analysis of proteomic data. Submitted.

Efron, B., and Tibshirani, R. (1996). Using specially designed exponential families for density estimation. Annals of Statistics, 24, 2431–2461.

Wand, M.P. (1997). Data-based choice of histogram bin width. American Statistician, 51, 59–64.