EVTr

Injured athletes or performers can cost teams, sports associations, and coaches a lot of money. Therefore, it can be useful to predict the number of seriously injured athletes and the length of these injuries at the start of a season or year. It turns out that individuals (especially professional athletes) are injured all the time and often get better within the day or the week. However, we are interested in long term injuries that last a season or many years since these are the most costly. The problem is that these types of injuries happen the least. Similar to massive earthquakes and stock market crashes, how do we model these types of scarce and infrequent injuries?

We use extreme value theory - and specifically the peaks-over-threshold method - to model this type of process. To begin, we do various simulation studies to study how various distributional assumptions, censoring, and data manipulations can affect estimation. We assume that individuals live in two states - they can either be injured or healthy. Individuals start healthy (or in a healthy state) and then remain healthy for a while until they switch to being injured (or in an injured state). Individuals continue alternating between these two states until our study is over (or censoring occurs). Then we use extreme value theory to study these injury periods. Specifically, we ask

• Does censoring matter? Can we assume the censored injury was not censored and use MLE normally?
• Will the censored injury be the longest injury and therefore should censoring be taken into account?
• What is the proportion of injuries being censored as appose to healthy periods? Will the distribution of the injuries/healthy periods play a roll in this proportion?

This package accompanies a masters thesis called “Using extreme value theory to model severe injuries of circus artists”.

Installation

The development version from GitHub can be installed with:

# install.packages("devtools")
devtools::install_github("aredelmeier/EVTr")

To install the package and also download the vignette use:

# install.packages("devtools")
devtools::install_github("aredelmeier/EVTr", build_vignettes = TRUE)

Then, you can access the vignette using:

vignette("understanding_EVTr",package = "EVTr")

Once the package is loaded, find help on the most important functions in the package using:

library(EVTr) # load package
help(EVTr)

To find specific help on one of the functions use (with correct name of function):

help(mle)

Example

This is a basic example which shows you how to solve a common problem:

library(EVTr)

df <- gen_data(censor = 10,
         xi = 1,
         n = 5,
         num_inj = 5,
         rate_exp = 1,
         ne = NULL,
         specific = c("delete_censored_obs"),
         seed = 1)

Then you can easily calculate the non-censored genearlized Pareto distribution MLE with:

# non-censored MLE
mle(data = df, method = "MLE")
#> [1] 0.21929

Or the censored MLE with:

# censored MLE
mle(data = df, method = "CensMLE")
#> [1] 0.21929