# Statistical analysis


## Description

This repository contains source code of two documents

- `lectures`: an summary of the lectures of the course

- `notes`: an explanation of the solutions of the exercises

and the programs written for each exercise (`ex-n` directories)


## Building the documents

The two documents `excercise.pdf` and `lectures.pdf` are written in Pandoc
markdown. XeTeX (with some standard LaTeX packages), the
[pandoc-crossref](https://github.com/lierdakil/pandoc-crossref) filter and a
Make program are required to build. Simply typing `make` in the respective
directory will build the document, provided the above dependencies are met.


## Building the programs

The programs used to solve the exercise are written in standard C99 (with the
only exception of the `#pragma once` clause) and require the following
libraries to build:

- [GMP](https://gmplib.org/)

- [GSL](https://www.gnu.org/software/gsl/)

* [pkg-config](https://www.freedesktop.org/wiki/Software/pkg-config/)
  (build-time only)

Additionally Python (version 3) with `numpy` and `matplotlib` is required to
generate plots.

For convenience a `shell.nix` file is provided to set up the build environment.
See this [guide](https://nixos.org/nix/manual/#chap-quick-start) if you have
never used Nix before. Running `nix-shell` in the top-level will drop you into
the development shell.

Once ready, invoke `make` with the program you wishes to build. For example

    $ make ex-1/bin/main

or, to build every program of an exercise

    $ make ex-1

To clean up the build results run

    $ make clean


## Running the programs

Notes:

- Many programs generate random numbers using a PRNG that is seeded with a
fixed value, for reproducibility. It's possible to test the program on 
different samples by changing the seed via the environment variable
`GSL_RNG_SEED`.


### Exercise 1

`ex-1/bin/main` generate random numbers following the Landau distribution and
run a series of test to check if they really belong to such a distribution.

The size of the sample can be controlled with the argument `-n N`.

The program outputs the result of a Kolmogorov-Smirnov test and t-tests
comparing the sample mode, FWHM and median, in this order.